1-3 Solving Addition and Subtraction Equations Pre-Algebra Warm Up Write an algebraic expression for each word phrase. 1. a number x decreased by 9 2.

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

Warm UpWrite 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

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

Learn to solve equations using addition and subtraction.

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

Vocabularyequationsolvesolutioninverse operationisolate the variableAddition Property of EqualitySubtraction Property of Equality

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

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.

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

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

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

Additional Example 1: Determining Whether a Number is a Solution of an Equation

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?

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

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

Additional Example 1 Continued

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?

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

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

Additional Example 1 Continued

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 ?

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

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.

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

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

1-3 Solving Addition and Subtraction Equations

Pre-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

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

Solve.

Additional Example 2A: Solving Equations Using Addition and Subtraction Properties

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?

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

Solve.

Additional Example 2B: Solving Equations Using Addition and Subtraction Properties

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?

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

Solve.

Additional Example 2C: Solving Equations Using Addition and Subtraction Properties

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?

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

Solve.

Try This: Example 2A

Subtract 15 from both sides.

A. 15 + n = 2915 + n = 29

–15 –15

0 + n = 14 n = 14 Identity Property of Zero: 0 + n = n.

Check

15 + n = 29 ?

10 + 14 = 2929 = 29

?

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

Additional Example 3A

+ =+ =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

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

Additional Example 3B

+ =+ =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

1-3 Solving Addition and Subtraction Equations

Pre-Algebra

Try This: Example 3A

+ =+ =27 535

x + 0 = 508

A. Isabelle earned $27 interest and now has a balance of $535 in the bank. What was her balance before interest was added?

Subtract 27 from both sides.

x + 27 = 535

Isabelle had a balance of $508 before interest was added.

balance before interest

interest earned

x

–27 – 27

x = 508

Solve:

balance after interest