3-2 Solving Inequalities Using Addition or Subtraction

3-2 Solving Inequalities Using Addition or Subtraction

page 171

10/13/20

Objective: To use addition or subtraction to solve inequalities.

Just as we used properties of equality to solve equations, we can use properties of inequalities to solve inequalities.

Equivalent inequalities are inequalities that have the same solution.

Do you think there is an addition/subtraction property of inequalities?

Add the same number to both sides of the inequalities to find out.

3 < 8

add 2 to both sides is it still true?

3 +2 < 8 +2

subtract 5 from both sides is it still true?

3 -5 < 8 -5

YES!

-5 > -7

add 4 to both sides is it still true?

-5 +4 < -7 +4

subtract 5 from both sides is it still true?

-5 - 5 < -7 -5

Addition/Subtraction Property of Inequality

if an inequality exists, adding or subtracting the same number on both sides does not change the inequality.

Multiple Choice

What are the solution to n - 5 < -3

• n < -8

• n < -2

• n < 8

• n < 2

Multiple Choice

How do you graph the solution from problem 1 got it?

n < 2

Multiple Choice

What are the solutions of

 $-1\ \ge y+12$  

•  $y\ge11$  

•  $-13\ge y$  

•  $11\ge y$  

•  $y\ge13$  

Multiple Choice

Which inequality is equivalent to the inequality from problem 3 got it?
 $-13\ge y$  

•  $-13\le y$  

•  $y\le-13$  

•  $y\ge13$  

Multiple Choice

What is the correct graph for the solution of the problem 3 got it? question?

Multiple Choice

Johnny earns $15 per hour dog walking. He wants to earn at least $105 to buy a new bike. Which inequality represents how long Johnny needs to work to afford his new bike? 

• 15h ≤ 105
• 15h > 105
• 15h < 105
• 15h ≥ 105

Multiple Choice

Solve the following then choose the matching graph.

n + 1 ≤ 7

• A

• B

• C

• D

Multiple Choice

To stay within the budge, the area of the house and garage combined is at most 3000 square feet. The area of the garage is 528 square feet. Write and solve an inequality that represents the area of the house.

• a ≤ 2,472 square feet
• a < 2,472 square feet
• a ≥ 1,587 square feet
• a < 3,467 square feet

Multiple Choice

Andrew has saved $55 toward the purchase of an IPOD. The IPOD costs $145. Which equation represents the amount Andrew needs to save to by the IPOD?

• 55 + x = 145
• 145x = 55
• 55 - x = 145
• 145 (55) = x

Multiple Choice

Joey and four of his friends went out to eat. They decided to split the bill evenly. Each person paid $11.13. Let b represent the total bill.

• b + 5 = 11.13

• b - 5 = 11.13

• b/5 = 11.13

• 5b = 11.13

Multiple Choice

Mrs. Scott decided that she would spend no more than $120 to buy birthday presents for her triplets. Which inequality can be used to determine the maximum Mrs. Scott can spend on each child?

• 3x > 120

• 3x ≤ 120

• x + 3 ≤ 120

• x + 3 > 120

Multiple Choice

Does the given value make the inequality true?  x + 9 > 21, when x = 15

• True
• Not True

Multiple Choice

r - 14 ≥ 17

• r ≥ 3
• r ≥ -31
• r ≥ 31
• r ≥ -3

Multiple Choice

When solving an equation that uses addition, such as t + 8 = 20, what inverse operation should you use to solve for t?

• Addition

• Subtraction

• Multiplication

• Division