Chapter 7 Lesson 4Solving Inequalities

by Adding or Subtracting

pgs. 345-349

Chapter 7 Lesson 4Solving Inequalities

by Adding or Subtracting

pgs. 345-349

What you’ll learn:Solve inequalities by using the Addition or

Subtraction Properties of Inequality

What you’ll learn:Solve inequalities by using the Addition or

Subtraction Properties of Inequality

Solving an inequality means finding values for the variable that make the inequality true.

You can solve inequalities by using the Addition and Subtraction Properties of Inequalities (pg. 345) This is the same concept as using the Addition/Subtraction Properties of Equations (Lesson 3-3 pgs. 110-111)

Solving an inequality means finding values for the variable that make the inequality true.

You can solve inequalities by using the Addition and Subtraction Properties of Inequalities (pg. 345) This is the same concept as using the Addition/Subtraction Properties of Equations (Lesson 3-3 pgs. 110-111)

Example 1: Solving an Inequality using Subtraction

Example 1: Solving an Inequality using Subtraction

Solve -13 9 + b Check your solutionSolve -13 9 + b Check your solution

Write the inequality: -13 9 + b

Subtract 9 from each side: -13 9 + b -9 -9

Simplify: -22 b or b -22To check your solution, try any number less than or equal

to -22

Check using -22:-13 9 + (-22)-13 -13

Check: using -30-13 9 + -30-13 -21

Check using -20:-13 9 + -20-13 -11

Example 2: Solving an Inequality using AdditionExample 2: Solving an

Inequality using Addition

Solve a - 5 6 Check your solution Solve a - 5 6 Check your solution

Write the inequality: a - 5 6

Add 5 to both sides: a - 5 6 +5 +5

Simplify: a 11

Check your result by using any number greater than 11

Check using 12:12 - 5 67 6

Check using 32:32 - 5 627 6

Check using 7:7 - 5 62 6

Example 3: Graph Solutions of Inequalities

Example 3: Graph Solutions of Inequalities

Solve h + 4 4 Then graph the solution on a number line.

Solve h + 4 4 Then graph the solution on a number line.

Write the inequality: h + 4 4Subtract 4 from each side: h + 4 0

- 4 -4 h 0

The solution is h 0

Check: any number greater than 0I’m using 11 + 4 4 5 4

Now graph the solutionOn a number line.

Done on board in class.

Example 4: Use an Inequality to Solve a

Problem

Example 4: Use an Inequality to Solve a

ProblemChris is saving money for a ski trip. He

has $62.50, but his goal is to save at least $100. What is the least amount Chris needs to save to reach his goal?

Chris is saving money for a ski trip. He has $62.50, but his goal is to save at least $100. What is the least amount Chris needs to save to reach his goal?

Explore: We need to find the least amount Chris needs to savePlan: Let x represent the amount he needs to save. Write

an inequality to represent the problem. Remember at least means greater than or equal to.

x + 62.50 100

Solve: x + 62.50 100 - 62.50 -62.50 x 37.50

So the least amount that Chrisneeds to save is $37.50

Your Turn! Solve the inequality, graph your solution, do a check

Your Turn! Solve the inequality, graph your solution, do a check

A. c - (-2) 3

B. 25 n + (-12)

C. g - 1 2

D. k + 9 -21

A. c - (-2) 3

B. 25 n + (-12)

C. g - 1 2

D. k + 9 -21

2 3

16

c + 2 3 Check using -1 -2 -2 -1 - (-2) 3 c 1 13

25 n + (-12) Check using 40+12 +12 25 40 + (-12) 37 < n , n 37 25 28

g - 5 + 5 13 + 5 Check using 4 3 3 6 3 4 - 1 2 g 3

2 2

23

16

13

16k + 9 -21 Check using -25

- 9 -9 -25 + 9 -30 k -30 -16 -30

56

Extra Practice by the door on your way out. See me if you have questions/problems!

Extra Practice by the door on your way out. See me if you have questions/problems!