Solving Inequalities by Addition & Subtraction

Objective:7.5.03

Essential Question: How can we use inverse operations

to solve one step addition and subtraction inequalities?

Solving Inequalities by Addition & Subtraction

Review:Solving Inequalities by Addition & Subtraction

<- is less

than

- is fewer than

>- is more

than

- is greater than

≤- is less

than or equal to

- is no more than

≥- is greater

than or equal to

- is no less than

Real World:Brandi has $30 to spend on food and rides at a carnival. She has already spent $12 on food. Write an inequality and determine how much money she can spend on rides

Inequality: m + 12 ≤ 30m ≤ 18

Brandi can spend up to $18 on rides.

Solving Inequalities by Addition & Subtraction

Example 1: Solve x + 3 > 9.

x + 3 > 9

Solving Inequalities by Addition & Subtraction

Example 1: Solve x + 3 > 9.

x + 3 > 9 – 3 – 3

x > 6

Solving Inequalities by Addition & Subtraction

Example 1: Solve x + 3 > 9.

x + 3 > 9 – 3 – 3

x > 6

4 5 6 7 8

Solving Inequalities by Addition & Subtraction

Example 2: Solve x – 3 < 9.

x – 3 < 9

Solving Inequalities by Addition & Subtraction

Example 2: Solve x – 3 < 9.

x – 3 < 9 + 3 + 3

x < 12

Solving Inequalities by Addition & Subtraction

Example 2: Solve x – 3 < 9.

x – 3 < 9 + 3 + 3

x < 12

10 11 12 13 14

Solving Inequalities by Addition & Subtraction

Example 3: Solve x + 3 ≥ – 9.

x + 3 ≥ – 9

Solving Inequalities by Addition & Subtraction

Example 3: Solve x + 3 ≥ – 9.

x + 3 ≥ – 9 – 3 – 3

x ≥ – 12

Solving Inequalities by Addition & Subtraction

Example 3: Solve x + 3 ≥ – 9.

x + 3 ≥ – 9 – 3 – 3

x ≥ – 12

-14 -13 -12 -11 -10

Solving Inequalities by Addition & Subtraction

Example 4: Solve 12 + m ≤ 4.

12 + m ≤ 4

Solving Inequalities by Addition & Subtraction

Example 4: Solve 12 + m ≤ 4.

12 + m ≤ 4 – 12 – 12

m ≤ – 8

Solving Inequalities by Addition & Subtraction

Example 4: Solve 12 + m ≤ 4.

12 + m ≤ 4 – 12 – 12

m ≤ – 8

-10 -9 -8 -7 -6

Solving Inequalities by Addition & Subtraction

Independent Practice:Write an inequality and graph.1. Two more than a number is less than eleven

2. Five less than a number is at least – 2

3. The difference between a number and ten is greater than 9

4. Four less than a number is less than 11

5. The sum of a number and seven is more than 1

Solving Inequalities by Addition & Subtraction

Independent Practice:Answers.1. n < 9 1.

2. n ≥ 3 2.

3. n > 19 3.

4. n < 15 4.

5. n > – 6 5.

9

3

9

15

- 6

Solving Inequalities by Addition & Subtraction

Independent Practice:Solve each equation below.

1. y + 8 ≤ 122. d + 11 > 303. 4 + a ≥ – 14. 5 < 1 + k5. h – 3 ≤ – 3

Solving Inequalities by Addition & Subtraction

Independent Practice:Answers.

1. y + 8 ≤ 12 1.2. d + 11 > 30 2.3. 4 + a ≥ – 1 3.4. 5 < 1 + k 4.5. h – 3 ≤ – 3 5.

4

19

- 5

4

0

Solving Inequalities by Addition & Subtraction

HOMEWORK

Solving Inequalities by Addition & Subtraction