August 4, 2008

- Show “Beginning Notes” PowerPoint presentation.

August 5, 2008

Continue Beginning Notes.

August 6, 2008

Finish Beginning Notes

Assign textbooks

August 7, 2008

Basics Quiz

Collect Notes.

Basics Quiz

1. What three things should be on the heading of everything you turn in?

2. What will be your grade on the “Guidelines” sheet if you turn it in exactly one week from today?

3. How long do you have to turn in make-up work for full credit?

4. What math test do you have to pass in order to graduate? Will you take it at the end of this class?

5. When is it ok to talk while the teacher is talking?

6. When is it ok to get up out of your seat while the teacher is talking?

7. What is the penalty for one tardy? For two?

8. What counts more for your final grade – your classwork average or your test average?

9. What two things did Mr. Allred say he is going to be very strict about in this class? (He actually said he’d be a real jerk about it!)

10. What do you want from this class?

11. What are you going to do to get it?

Bellwork: Overhead problems

If you have a seating preference, put it on a sheet of paper and give to me now. A seating chart will be implemented soon.

Complete Exercises 2 – 18 even, page 2. Write out the problems (except 18)

Notes: Using Variables

Objective: Model Relationships with Variables.

Model Relationships with Equations and Formulas.

Simplify and Evaluate Expressions with and without Grouping Symbols.

Tennessee Curriculum Standards:

Variable – symbol representing an unknown quantity.

Algebraic expression – mathematical phrase containing numbers, symbols, and operation signs.

- You will need to convert word phrases into algebraic expressions.

- Use key words to decide. (“a number”, twice, total, difference, etc.)

Write expressions for:

1. Eight more than a number.

2. The difference between twice a number and 12.

Problem 1. Write expressions for:

1. The sum of 6 and a number.

2. The quotient of a number and 5.

3. Three times the difference between a number and 9.

Equation

- A math expression that uses an “=” (balance)

- In written words, “is” usually means “=”

Open sentence

- An equation with one or more variables.

- Model a relationship with an equation by interpreting the words

o A store sells CD’s for 18.99 each. Write an equation to model the cost if you buy x CD’s.

o Define variables. These are the things you don’t know. (Cost and number of cd’s you buy.)

o C = 18.99 x

Problem 2. Write an equation for the perimeter of a stop sign is 8 times the length of a side.

Exponents/ Order of Operations

Simplify everything if you can.

- Means “find the answer”

- add, subtract, multiply, and divide until you have the simplest answer possible.

- Exponent (define base, exponent, and power)

o Simplify 5² 5 ●5 = 25

o Squared, Cubed

Order of Operations

- PEMDAS

12 – 5 + 3

23 - 15 + 4 ● 2

3 + 4 (7 + 3)

Problem 3. Simplify 15 - 3² + 8 and 4 + 6(2 + 8)

A = 3, B = 4, C = 5

2A + B² – (3C – 10)

(AB – C)²

A fraction bar is a grouping symbol too.

3 ( 5 + (9 – 4)

6 + 3²

P - 2l = w For P = 60 and L = 25

Assignment: Section 1-1, page 6, problems 2 – 16, 26 – 38, even only.

Section 1-2, page 12 – 13, problems 3 – 60, every 3^rd problem, and omit 27 and 54.

August 8, 2008

Bellwork: Overhead Problems

Complete exercises 89 – 106, omit 99 and 100.

Notes: Real Numbers

Objective: Classify and Compare Numbers

Tennessee Curriculum Standards:

Classifying #’s

- Natural #’s (1, 2, 3, …)

- Whole #’s (0, 1, 2, 3, …)

- Integers (…-2, -1, 0, 1, 2, 3, …)

- Rational #’s Any # that can be written as a/b

- Irrational #’s Can’t be written as a/b (π)

- Real #’s (Combination of Ration and Irrational)

Problem 1. Name all sets of numbers that these belong in.

8, -5, 3 ½, pi, -2.5, 3.3…

Comparing #’s

Inequalities >< or = > < or not equal

(Show on a number line)

Comparing fractions

- Must find common denominators OR change to decimal

- 5/12 ____ 3/8

Problem 2. Write the fractions in order from least to greatest.

1/12, -2/3, -5/8

Opposites 5 and -5

Sum of opposites is always zero

Absolute value

- distance from zero on a number line

- Always positive

- Treat like parenthesis in order of operations

Problem 3. |-4| + 7 and | -15 | - | 8 |

Assignment: Section 1-3, page 20 - 21, problems 1 – 60.

August 11, 2008

Bellwork: Overhead Problems

1. How should you address a teacher or any adult?

Exercises 1 – 12, page 24.

Notes: Adding Real Numbers

Objective: Add Real Numbers using Models and Rules

Apply Addition Properties to Expressions

Tennessee Curriculum Standards:

(Remember natural, whole, integer, rational, and irrational?)

Addition properties

Identity N + 0 = N

Inverse N + -N = 0

Adding integer rules

P + P = P Add

N + N = N Add

N + P = Sign of larger # Subtract

(Similar to in a football game. Gains can be represented as positive numbers and losses as negative numbers.)

Problem 1. Find the sum.

a. 3 + -11 =

b. -12 + -5 =

c. 3 + 2 =

Applying Addition

-A + 12 for A = 5

-M – 7 for M = -2

Problem 1. Death Valley is 284 feet below sea level. A helicopter rises 1000 feet from the floor of Death Valley. What is the helicopter’s height above sea level?

Adding Matrices

Matrix – a rectangular arrangement of numbers.

Size – number of rows by number of columns.

Are equal if all corresponding elements are equal.

To add matrices, they must be equal sized. Add all corresponding elements together.

Problem 2. [2 5 -3] + [-2 0 1]

[-8 -7 -6] [3 -5 7]

Assignment: Section 1 – 4, page 28 – 29, 6 – 91, every 3^rd problem, omit 84, 94 – 98 all.

August 12, 2008

Bellwork: Overhead Problems

What is the polite thing to do when someone asks you a question about yourself?

Exercises 1 – 8, page 32.

Notes: Subtracting Real Numbers

Objective: Subtract Real Numbers.

Apply Subtraction to Expressions

Tennessee Curriculum Standards:

Subtraction is BAD!

Addition is GOOD!

There are no rules for subtracting numbers.

- To subtract a number, add it’s opposite.

o Change minus to a plus

o Change the sign of the next number

o Follow the rules for adding real numbers.

Problem 1. 7 – 12, -5 - - 9, -8 - -15,

With absolute value signs, treat them like parenthesis.

|7 - 13| = |7 + - 13| = |-6|

Problem 2. |-5 - 18|

Evaluating Expressions

M = -5, N = -2

Find – M – N (Substitute the numbers for the variables and solve.)

- (-5) – (-2)

Assignment: Section 1 – 5, page 34 – 35, 1 – 57, omit 19, 20, 51 - 54.

August 13, 2008

Bellwork: Overhead Problems

If someone is speaking to you, make sure that you ______ ______ ______.

Exercises 1 – 8, page 37.

Notes: Multiplying and Dividing Real Numbers

Objective: Multiply Real Numbers

Divide Real Numbers

Tennessee Curriculum Standards: 1.1, 1.3, 2.1, 2.2, 2.7, 3.14

Properties Of Multiplication

Identity M ● 1 = M

Zero M ● 0 = 0

-1 M ● -1 = -M

Inverse M ● 1/M = 1

(Additive inverse 5 and -5)

(Multiplicative inverse 5 and 1/5, same as reciprocal)

P ● P = P

N ● N = P

N ● P = N

Every pair of negative numbers cancel out.

Same rules for division.

Problem 1. – ¾ * 2/3 =

-2 * -5 * -3 * -1 =

Evaluating expressions

A = -2, B = -3, C = -4

AB = ?

-3 C = ?

- A ● B ● – C = ?

Problem 2. 2x + (x - 1)/(y + 2) for x = -1 and y = -1

Exponents

-2⁴ = -(2●2●2●2) = -16

(-2)⁴ = -2●-2●-2●-2 = 16

Division using reciprocals

-2/3 ÷ 3/4 =

-2/3 ● 4/3 =

Assignment: Section 1 – 6, page 41 - 42, 1 – 84, omit 31, 37, 39, 45, 50, 52 -57, 63, 65, 70 - 79.

August 13, 2008

Bellwork: Overhead Problems

If someone is speaking to you, make sure that you ______ ______ ______.

Exercises 1 – 8, page 37.

Notes: Multiplying and Dividing Real Numbers

Objective: Multiply Real Numbers

Divide Real Numbers

Tennessee Curriculum Standards: 1.1, 1.3, 2.1, 2.2, 2.7, 3.14

Properties Of Multiplication

Identity M ● 1 = M

Zero M ● 0 = 0

-1 M ● -1 = -M

Inverse M ● 1/M = 1

(Additive inverse 5 and -5)

(Multiplicative inverse 5 and 1/5, same as reciprocal)

P ● P = P

N ● N = P

N ● P = N

Every pair of negative numbers cancel out.

Same rules for division.

Problem 1. – ¾ * 2/3 =

-2 * -5 * -3 * -1 =

Evaluating expressions

A = -2, B = -3, C = -4

AB = ?

-3 C = ?

- A ● B ● – C = ?

Problem 2. 2x + (x - 1)/(y + 2) for x = -1 and y = -1

Exponents

-2⁴ = -(2●2●2●2) = -16

(-2)⁴ = -2●-2●-2●-2 = 16

Division using reciprocals

-2/3 ÷ 3/4 =

-2/3 ● 4/3 =

Assignment: Section 1 – 6, page 41 - 42, 1 – 84, omit 31, 37, 39, 45, 50, 52 -57, 63, 65, 70 - 79.

August 14, 2008

Page 67 – 68, 1 – 37, omit 10, 11, and 12.

Page 702, 1 – 53, omit 48 – 51.

All work is due at the end of class. Students must write out the problems and show their work – it doesn’t matter how easy it is! Work will not be accepted tomorrow! Due today!

August 15, 2008

Bellwork: Overhead Problems

Page 47, 1 - 6

Notes: The Distributive Property

Objective: Use the Distributive Property.

Simplify Algebraic Expressions

Tennessee Curriculum Standards: 1.1, 2.1, 2.3, 3.14

The Distributive Property

A(B+C) = AB + AC

MN + MP = M(N+P)

Can simplify problems with this…

31(203) = 30 * 203 + 1 * 203

23 (97) = 23 * 100 – 23 * 3

Problem 1. 13 (103) and 24 (98)

Vocabulary

Term - #, variable, or product of the two.

Constant – a number.

Variable – symbol for an unknown quantity.

Coefficient – a number multiplying by a variable

Like Terms – terms with same variables and exponents. Can Add!

Unlike Terms – terms with different variables or exponents. Can’t Add!

(show many examples of like and unlike terms)

Problem 2. -8a + 15a

Simplifying Expressions

5 (3x - 6)

(8 – 4x) (-5)

Assignment: Section 1 – 7, page 50, 1 – 4, 15 – 57, omit 48 and 54.

Do not do

Bellwork: Overhead Problems

Page 52, 105 – 110, 121 -123.

Notes: Review like and unlike terms, the distributive property, and simplifying.

Assignment: In class participation: Class will work one problem at a time. Problems progress from simple combining like terms, to multiplying a term by a constant, to using the distributive property, to using the distributive property with terms added.

Examples: 5x + 7

5x + 7x

-3 (5x)

-5 (3x – 2)

5h – 7 (4h – 3)

Page 50, problems 16 – 55, every third problem, omit 49.

(Do this for make up work.)

August 18, 2008

Bellwork: Overhead Problems

Page 54, 1 – 9.

Notes: Properties of Real Numbers

Graphing and Scatter Plots

Objective: Identify Properties.

Graph Points on a Coordinate Plane

Analyze Data Using Scatter Plots

Tennessee Curriculum Standards:

Properties of Algebra

Commutative

Associative

Identity

Inverse

Distributive

Multiplication property of zero

Multiplication property of -1

Graphing Points on a coordinate plane

Coordinate plane

X – axis

Y – axis

Origin

Quadrants

Point, Ordered Pair, Coordinate

Scatter Plot

Plot that relates two groups of data

Positive, Negative, and No relationships

Trend Line – shows pos/neg relationships on a scatterplot.

Age of car/ Value of car Negative Relationship

Age of car/ Total mileage Positive Relationship

Age of car/ Color of car No relationship

Other examples

Age of person/ IQ

Height of person/ weight

Age of person/ number of diapers used

Review Chapter One Concepts

Assignment: Section 1 – 8, page 56 – 57, 1 – 35 complete the first 4 problems of each section, omit 17, 18, (look at 26), 40 - 44.

Section 1 – 9, page 62 - 63, 1 – 22, 29 - 33.

Pg. 67 – 69, all vocabulary and ½ problems in each section for 10 points extra credit.

August 19, 2008

Bellwork: Overhead Problems

Page 70, complete any eight problems – one per section.

Make your notes ready to use on the test. You should have 7 sections of notes.

Notes: None.

Get your notes ready to be graded.

1. Using Variables

2. Real Numbers

3. Adding Real Numbers

4. Subtracting Real Numbers

5. Multiplying and Dividing Real Numbers

6. The Distributive Property

7. Properties of Real Numbers

- Graphing and Scatter Plots

Assignment: Chapter 1 Test

Omit: 1, 2, 10, 12, 14 – 17, 21, 23, 26, 29, 30, 32, and 35.

Extra Credit: The best/worst movie ever made is…

To get credit, you must answer with a minimum of 4 complete sentences telling me your opinion of why you believe what you do.

August 20, 2008

Bellwork: Overhead Problems

Page 74, 1 – 8.

Notes: One Step Equations

Objective: Solve Equations Using Addition, Subtraction, Multiplication, and Division.

Tennessee Curriculum Standards: 1.1, 1.3, 1.4, 2.1, 2.3, 2.5, 2.8, 3.5, 3.11, 3.14

Equation – balance between both sides of the equals sign.

General Idea – get rid of stuff with the variables.

Method – whoop some math on it.

- Always simplify if possible.

Solving addition/subtraction equations

- Change subtraction to addition/ change sign of next number.

- Get rid of thing being added.

- Add it’s opposite to both sides of the equals sign.

- Simplify

Problem 1. Solve for x.

X + 12 = 3 -17 = x - 7

Solving Multiplication Equations

- Get rid of thing being multiplied.

- Divide everything by the exact same number

- Simplify

Solving Division Equations

- Get rid of thing being divided.

- Multiply everything by the exact same number.

- Simplify

Problem 2. Solve for x.

8x = -240 x/-4 = -3

With a fraction coefficient…

- Get rid of the fraction by multiplying everything by its reciprocal.

Problem 3. Solve for x.

¾ x = 6 10 = -2/3 x

Assignment: Section 2-1, page 77-78, 3-69, omit 17 – 20, 25, 33, 36 – 38, 53, 54, 57, 60, 61, 64, 66, and 69.

August 21, 2008

Bellwork: Overhead Problems

(In class activity)

Inverse Operations Bingo

August 21, 2008 (3^rd block) August 22, 2008 (4^th Block)

Bellwork: Overhead Problems

Page 81, 1 – 9.

Notes: Two-Step Equations

Objective: Solve Two Step Equations

Tennessee Curriculum Standards: 1.4, 2.1, 2.3, 3.11, 3.14

Solve for the variable by:

- Get rid of added term by adding it’s opposite.

- Get rid of multiplied coefficient by dividing by the same number.

- Get rid of divisor by multiplying by the same number.

- Get rid of a negative sign on the variable by (mentally) multiplying each term by -1.

Must show inverse step!

Problem 1. 4x – 12 = 8 3 = x/-6 - -9

Assignment: Section 2-2, page 84-85, 3 – 42, every third problem, omit 36 and 39, and 67.

August 22, 2008 (3^rd Block) August 25, 2008 (4^th Block)

Bellwork: Overhead Problems

Page 88, 1 – 10.

Notes: Solving Multi-step Equations Part I

Objective: Use the Distributive Property to Combine Like Terms and to Solve Equations.

Tennessee Curriculum Standards: 1.4, 2.3, 3.11, 3.14

Review 2-step equations

- get rid of added terms by adding it’s opposite

- get rid of multiplied or divided coefficient by doing the opposite operation with the same #.

Combining like terms first

2x + 8 – 5x = -10

-3x + 8 = -10

Now solve like a normal 2-step equation.

Problem 1. -3x + 8 + -2x = -12

Using the distributive property to solve equations

5(2m – 3) - 9 = 36

10 m + -15 + -9 = 36

10 m + -24 = 36

Problem 2. 15 = -3(x - 1) + 9

Assignment: Section 2-3, page 91, 1-20, omit 10 and 11.

August 25, 2008 (3^rd Block) August 26, 2008 (4^th Block)

Bellwork: Overhead Problems

1. 32 = -3x + 5

2. -12m – 5 + 8m = -29

3. 23 = 3A + -4(2A – 2)

Notes: Solving Multi-step Equations Part II

Objective: Use the Distributive Property to Combine Like Terms and to Solve Equations.

Tennessee Curriculum Standards: 1.4, 2.3, 3.11, 3.14

Fraction Basics (Should know this by now- review)

Mixed to improper

Improper to mixed

Adding/Subtracting

Multiplying/Dividing

Solving problems with fractions (2 ways)

2/3x + -x/4 = 10 1. Find common denominators

8/12 x + -3/12x = 10

5/12 x = 10

● 12/5 ● 12/5

x = 24

2/3x + -x/4 = 10 1. Multiply to clear fractions

12(2/3x + -x/4) = (10)12 (common denominator is 12)

8x + -3x = 120

5x = 120

x = 24

Problem 1. Solve.

3/4x + 5/6 = 2/3

Solving Equations with Decimals

0.3x + 0.75 = -0.15 (Multiply by 10 to the power of the number of decimal places in the number with the greatest amount of decimal places)

100(0.3x + 0.75) = (-0.15)100

30x + 75 = -15

30x = -90

x = -3

Problem 2. -1.8x – 3.2 = 0.4

Assignment: Section 2-3, page 91, 22-52 even, add 51.

August 26, 2008 (3^rd Block)

Bellwork: Overhead Problems

Page 94, 74 - 95

Notes: Review Multi-Step Equations

Objective: Use the Distributive Property to Combine Like Terms and to Solve Equations.

Tennessee Curriculum Standards: 1.4, 2.3, 3.11, 3.14

2-step with:

Combining like terms.

The distributive property.

Fractions.

Decimals.

Assignment: Section 2-3, page 92, 39 – 62, omit 45 – 49, 53, and 55.

August 27, 2008

Bellwork: Overhead Problems

Page 96, 1-8

Notes: Solving Equations with Variables on Both Sides of the “=”

Objective: Solve Equations with Variables on Both Sides.

Identify Equations that are Identities or Have No Solutions.

Tennessee Curriculum Standards: 1.4, 2.1, 2.3, 2.5, 3.5, 3.11, 3.14

Use additive inverses to get variables on one side.

Follow all rules given so far!

- Subtraction is Bad!

- Simplify like terms

- Get rid of parenthesis (distributive property)

- Get rid of fractions.

- Get rid of decimals

- NOW – “letters to the left, numbers to the right”. (Suggestion).

Examples:

-6x = x + 4

2(c – 6) = 9c + 2

11x – 4 – 4x = 5 (x + 4) - 4

- It is possible to end up with 3 kinds of solutions

Examples:

7k – 4 = 5k + 16 (k = 10)

9 + 5n = 5n – 1 (no solution)

9 + 5x = 7x + 9 - 2x (identity)

Assignment: Section 2-4, page 98, 1 - 12.

August 28, 2008

Bellwork: Overhead Problems

Page 99, 22 – 27.

Notes: None

Assignment: Chapter 2 Sections 1 – 4 Test.

Omit any 2 problems

Extra Credit: Write a minimum of 4 complete sentences explaining what you think is the best or worst song ever written.

August 29, 2008

Bellwork: Overhead Problems (May begin to use calculators)

Page 99, 28 – 30, 41

Page 103, 1 – 5

Notes: Problem Solving

Objective: Define a Variable in Terms of Another Variable.

Model Distance, Rate, Time Problems.

Tennessee Curriculum Standards: 1.4, 2.4, 2.5, 2.6, 3.5, 3.6, 3.10, 3.11, 3.14, 5.1

Define one variable in terms of the other. (Problems with 2 or more unknown quantities)

- Perimeter of Rectangle = 16cm. Width is 2 cm less than the length. Find the length.

L = Length

W = L – 2 (define Width in terms of the length)

P = 2L + 2W

16 = 2L + 2(L + -2)

16 = 4L + -4

5 = L

- Consecutive Integers (Choose a variable to represent one of the integers and define the others in terms of that one. Consecutive integers are one apart. Consecutive even/odd integers are two apart.)

The sum of 3 consecutive integers is 48.

X = 1^st integer

X + 1 = 2^nd

X + 2 = 3^rd

X + X + 1 + X + 2 = 48

3x + 3 = 48

x = 15

- Distance Rate Time

D = RT

(See Check Understanding problem #3)

T = time the first canoe traveled

T – 2 time the 2^nd canoe traveled (define in terms of 1^st canoe)

Find both amounts of time.

Understand that both canoes traveled the exact same distance but different speeds. D = RT. D of 1^st = D of 2^nd. RT = R(T-2)

10 T = 22 (T + -2)

10 T = 22T + -44

-12T = - 44

T = 44/12 = 3 8/12 = 3 2/3

T – 2 = 1 2/3

Assignment: Section 2-5, page 107, 1 – 31, pick 3 of every 10 problems.

September 2, 2008

Bellwork: Overhead Problems

(May begin to use calculators.)

Page 100, #42

Page 111, 1 – 3.

Notes: Using Formulas

Objective: Transform Literal Equations

Find Mean, Median, and Mode.

Tennessee Curriculum Standards: 2.4, 2.5, 3.53.6, 3.14, 5.1

Formula – shows a relationship between quantities represented by variables.

E = MC²

A = πr²

C = πd

F = MA

V = 4/3 π r³

I = PRT

A = P(r + 1)ⁿ

A = ½ BH

D = RT

F = n/4 + 37

F = 1.8 C + 32

C = 5/9 (F – 32)

P = 2l + 2w

Literal equation – equation with 2 or more variables (like a formula).

Transforming an equation – solving for one of the variables in terms of the others.

- Use the rules you already know to solve for the variable.

Transforming a geometric equation

A = ½ BH For H (How do you get rid of a fraction coefficient?)

2/1 A = ½ BH 2/1

2A = BH (How do you get rid of the factor B?)

2A/B = H

Problem 1. Solve I = PRT for R

Transforming an equation

Y – 4 = 3x – 8 Solve for x.

(Add positive 8 to both sides; divide by 3 on both sides.)

Transforming equations with variables only.

V = IR Solve for r.

(Divide both sides by R.)

Two more examples.

C = 5/9 (F – 32) Solve for F.

D + T = $ + J Solve for $. (D = Ed.,T = spirit, E = Exercise)

Assignment: Section 2-6, page 113, 1 – 23 and 41.

September 3, 2008

Bellwork: Overhead Problems

Page 118, 1 – 6.

1. 6(2x + 2) - - 13 = 3x – 10 + 2x

Notes: Measures of Central Tendency

Objective: Make and Use Stem and Leaf Plots.

Identify or Calculate Mean, Median, and Mode.

Tennessee Curriculum Standards:

Mean – Average

Outlier – data that is much higher or lower than average/stands out.

Median – Middle number.

If there is an outlier, use the median. If no outlier, use the mean.

Mode - # that shows most often.

Use if data is not numeric or if survey answers.

Range – difference between greatest and least data

Stem and Leaf Plots

- A way to display and organize data

- Significant digits go on the stem.

- Back to back stem and leaf plots

Assignment: Section 2-7, page 121 - 122, problems 1-4, 9-12, 14 – 17, and 19.

September 4, 2008

No class

September 5, 2008

Bellwork: Overhead Problems

Page 128, # 22, 13, 14, 15.

Notes: None

Assignment: Test Review, in class activity. Page 125, 1 – 71.

September 8, 2008

Bellwork: Prepare notes and answer sheet for test.

Notes: None, brief review.

Assignment: Chapter 2 Test

You may omit any 3 problems.

Extra credit: If you could make one person live one moment of your life, who would you pick and what moment?

September 9, 10, 11, 12, 2008

Review during 3^rd and 4^th Block.

Complete Chapter 2 in 1^st Block.

September 15, 2008

Bellwork: Overhead problems

Page 134, 1 - 11

Notes: Inequalities

Objective: Identify Solutions of Inequalities.

Graph and Write Inequalities.

Tennessee Curriculum Standards: 1.2, 2.1, 3.6, 3.16

Solution – any number that makes the inequality true

X > 6 10, 7, 5² are solutions, 4, 0, 6 are not.

M < -5 -10, -6, and -5 are solutions, -4, 0, 12, are not.

Problem 1. Name 3 solutions to x < -3.5

Finding solutions by solving.

2 – 4A > 18 for A = -5