QuizEvaluate each expression for the given values of the variables.

1. 6x + 9 for x = 2

2. 4x + 3y for x = 4, y = 2

3. If n is the amount of money in a savings account, then the expression n + 0.05n can be used to find the amount in the account after it has earned interest for one year. Find the total in the account after one year if $100 is the initial amount.

Write an algebraic expression for each word phrase.

4. 8 less than a number k

5. 7 times the sum of n and 2

Write an algebraic expression and used it to solve the problem.

6. Tony buys n raffle tickets for $0.75 each. If he buys 12 of them, how much will they cost?

Pre-Algebra

Solving Addition and Subtraction Equations

1-3

Write an algebraic expression for each word phrase.

1. a number x decreased by 92. 5 times the sum of p and 63. 2 plus the product of 8 and n4. the quotient of 4 and a number c

x 95(p + 6)

2 + 8n4c

Warm Up

Learn to solve equations using addition and subtraction.

equationsolvesolutioninverse operationisolate the variableAddition Property of EqualitySubtraction Property of Equality

Vocabulary

An equation uses an equal sign to show that two expressions are equal. All of these are equations.

3 + 8 = 11 r + 6 = 14 24 = x – 7 1002

= 50

To solve an equation, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation.

Determine which value of x is a solution of the equation.

x + 8 = 15; x = 5, 7, or 23

Substitute each value for x in the equation.

Substitute 5 for x.13= 15 ?

So 5 is not solution.

x + 8 = 15?

5 + 8 = 15?

Determining Whether a Number is a Solution of an Equation

Determine which value of x is a solution of the equation.x + 8 = 15; x = 5, 7, or 23

Substitute each value for x in the equation.

Substitute 7 for x.15= 15 ?

So 7 is a solution.

x + 8 = 15?

7 + 8 = 15?

Example Continued

Determine which value of x is a solution of the equation.x + 8 = 15; x = 5, 7, or 23

Substitute each value for x in the equation.

Substitute 23 for x.31= 15 ?

So 23 is not a solution.

x + 8 = 15?

23 + 8 = 15 ?

Example Continued

Addition and subtraction are inverse operations, which means they “undo” each other.

To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

To solve a subtraction equation, like y 15 = 7, you would use the Addition Property of Equality.

You can add the same number to both sides of an equation, and the statement will still be true.

2 + 3 = 5+ 4 + 4

2 + 7 = 9

x = yx = y+ z + z

ADDITION PROPERTY OF EQUALITY

Words Numbers Algebra

There is a similar property for solving addition equations, like x + 9 = 11. It is called the Subtraction Property of Equality.

You can subtract the same number from both sides of an equation, and the statement will still be true.

4 + 7 = 11 3 3

4 + 4 = 8

x = yx = y z z

SUBTRACTION PROPERTY OF EQUALITY

Words Numbers Algebra

Solve.

Subtract 10 from both sides.

A. 10 + n = 1810 + n = 18

–10 –10

0 + n = 8 n = 8 Identity Property of Zero: 0 + n = n.

Check

10 + n = 18?

10 + 8 = 18

18 = 18?

Solving Equations Using Addition and Subtraction Properties

Solve.

Add 8 to both sides.

B. p – 8 = 9p – 8 = 9

+ 8 + 8

p + 0 = 17 p = 17 Identity Property of Zero: p + 0 = p.

Checkp – 8 = 9

? 17 – 8 = 9

9 = 9?

Solving Equations Using Addition and Subtraction Properties

Solve.

Add 11 to both sides.

C. 22 = y – 1122 = y – 11

+ 11 + 11

33 = y + 0 33 = y Identity Property of Zero: y + 0 = 0.

Check22 = y – 11

? 22 = 33 – 11

22 = 22?

Solving Equations Using Addition and Subtraction Properties

+ =+ =34 16,550

x + 0 = 16,516

A. Jan took a 34-mile trip in her car, and the odometer showed 16,550 miles at the end of the trip. What was the original odometer reading?

Subtract 34 from both sides.

x + 34 = 16,550

The original odometer reading was 16,516 miles.

odometer reading at the beginning of

the tripmiles traveled

x

–34 – 34

x = 16,516

Solve:

odometer reading at the end of the trip

+ =+ =n 1125

0 + n = 230

B. From 1980 to 2000, the population of a town increased from 895 residents to 1125 residents. What was the increase in population during that 20-year period?

Subtract 895 from both sides.

895 + n = 1125

The increase in population was 230.

initial population increase in population

895

–895 – 895

n = 230

Solve:

population after increase

Determine which value of x is a solution of the equation.

1. x + 9 = 17; x = 6, 8, or 26

2. x – 3 = 18; x = 15, 18, or 21

Solve.

3. a + 4 = 22

4. n – 6 = 39

5. The price of your favorite cereal is now $4.25. In prior weeks the price was $3.69. Write and solve an equation to find n, the increase in the price of the cereal.

821

a = 18

n = 45

3.69 + n = 4.25; $0.56

Lesson Quiz