1-8 Solving Equations by Adding or Subtracting

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Problem of the DayProblem of the Day

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1-8 Solving Equations by Adding or Subtracting

Warm UpAdd, subtract, multiply, or divide.

41 4

–4236

–8

1. 24 + 17 2. 23 – 19

3. 12 3 4. 6(–7)

5. 6. –250 + (–85)–64 8

–335

1-8 Solving Equations by Adding or Subtracting

Problem of the Day

Janie’s horse refused to do 5 jumps today and cleared 14 jumps. Yesterday, the horse cleared 9 more jumps than today. He won 3 first place ribbons. How many jumps did the horse clear in the two-day jumping event? 37

1-8 Solving Equations by Adding or Subtracting

Learn to solve equations using addition and subtraction.

1-8 Solving Equations by Adding or Subtracting

Vocabularyequationinverse operation

1-8 Solving Equations by Adding or Subtracting

An equation is a mathematical sentence that uses an equal sign to show that two expressions have the same value. All of these are equations.

3 + 8 = 11 r + 6 = 14 24 = x – 7 1002

= 50

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

1-8 Solving Equations by Adding or Subtracting

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

1-8 Solving Equations by Adding or Subtracting

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

1-8 Solving Equations by Adding or Subtracting

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

1-8 Solving Equations by Adding or Subtracting

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

To solve an equation, use inverse operations to isolate the variable. In other words, get the variable alone on one side of the equal sign.

1-8 Solving Equations by Adding or Subtracting

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

1-8 Solving Equations by Adding or Subtracting

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

1-8 Solving Equations by Adding or Subtracting

Solve.

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

Use the Subtraction Property of Equality: Subtract 10 from both sides.

10 + n = 1810 + n = 18

–10 –10

n = 8Check

10 + n = 18

10 + 8 = 1818 = 18

Substitute 8 for n.

1-8 Solving Equations by Adding or Subtracting

Solve.

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

Use the Addition Property of Equality: Add 8 to both sides.

p – 8 = 9p – 8 = 9

+ 8 + 8

p = 17Check

p – 8 = 9

17 – 8 = 9 9 = 9

Substitute 17 for p.

1-8 Solving Equations by Adding or Subtracting

Solve.

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

Use the Addition Property of Equality: Add 11 to both sides.

22 = y – 1122 = y – 11

+ 11 + 11

33 = yCheck

22 = y – 11

22 = 33 – 11

22 = 22

Substitute 33 for y.

1-8 Solving Equations by Adding or Subtracting

Jan and Alex are arguing over who gets to play a board game. If Jan, on the right, pulls with a force of 14 N, what force is Alex exerting on the game if the net force is 3 N?

Additional Example 3: Problem Solving Application

1-8 Solving Equations by Adding or Subtracting

Force is measured in newtons (N). The number ofnewtons tells the size of the force and the signtells the direction. Positive is to the right, and negative is to the left.

Helpful Hint!

1-8 Solving Equations by Adding or Subtracting

Net force Alex’s forceJan’s force= +

The answer is the force that Alex, on the left,

is exerting on the board game.

List the important information:• Jan, on the right pulls with a force of 14 N. • The net force is 3 N.

11 Understand the Problem

Show the relationship or the information:

Additional Example 3 Continued

1-8 Solving Equations by Adding or Subtracting

Write an equation and solve it. Let f represent Alex’s force on the board game, and use the equation model. 3 = f + 14

3 = f + 14Subtract 14 from both sides.

–11 = f

Alex was exerting a force of –11 N on the board game.

22 Make a Plan

Solve33

– 14 – 14

Additional Example 3 Continued

1-8 Solving Equations by Adding or Subtracting

Look Back44

Check the answer by using a number line. Move 14 units right to show Jan's force. Move 11 units to the left to show Alex's force.

Additional Example 3 Continued

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1411

1-8 Solving Equations by Adding or Subtracting

Frankie and Carol are playing tug of war using a rope. If Frankie, on the right, pulls with a force of 7 N, what force is Carol exerting on the game if the net force is 4 N?

Check It Out: Example 3

1-8 Solving Equations by Adding or Subtracting

Net force Carol’s forceFrankie’s force= +

The answer is the force that Carol, on the left is

exerting on the rope.

List the important information:• Frankie, on the right pulls with a force of 7 N. • The net force is 4 N.

11 Understand the Problem

Show the relationship or the information:

Check It Out: Example 3 Continued

1-8 Solving Equations by Adding or Subtracting

Write an equation and solve it. Let f represent Carol’s force on the rope, and use the equation model. 4 = f + 7

4 = f + 7Subtract 7 from both sides.

–3 = f

Carol was exerting a force of -3 N on the rope.

22 Make a Plan

Solve33

– 7 – 7

Check It Out: Example 3 Continued

1-8 Solving Equations by Adding or Subtracting

Look Back44

Check It Out: Example 3 Continued

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

7

3

Check the answer by using a number line. Move 7 units right to show Frankie's force. Move 3 units to the left to show Carol's force.