# 5-7 Solving Inequalities

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```					5-7 Solving Inequalities

Objective: Solve inequalities with
rational numbers.
5-Minute Check
Solve each equation. Check the solution.
1. n + 6.3 = -2.5
5-Minute Check
Solve each equation. Check the solution.
1. n + 6.3 = -2.5            -8.8
5-Minute Check
Solve each equation. Check the solution.
1. n + 6.3 = -2.5

2. 9.4 = w – 9.4
5-Minute Check
Solve each equation. Check the solution.
1. n + 6.3 = -2.5

2. 9.4 = w – 9.4             18.8
5-Minute Check
Solve each equation. Check the solution.
1. n + 6.3 = -2.5

2. 9.4 = w – 9.4

3. k – ¾ = -2/3
5-Minute Check
Solve each equation. Check the solution.
1. n + 6.3 = -2.5

2. 9.4 = w – 9.4

3. k – ¾ = -2/3              1/12
5-Minute Check
Solve each equation. Check the solution.
1. n + 6.3 = -2.5

2. 9.4 = w – 9.4

3. k – ¾ = -2/3

4. 4/5 = b – (-1/2)
5-Minute Check
Solve each equation. Check the solution.
1. n + 6.3 = -2.5

2. 9.4 = w – 9.4

3. k – ¾ = -2/3

4. 4/5 = b – (-1/2)          3/10
5-Minute Check
Solve each equation. Check the solution.
1. n + 6.3 = -2.5

2. 9.4 = w – 9.4

3. k – ¾ = -2/3

4. 4/5 = b – (-1/2)

5. 21/5 + p = 17/8
5-Minute Check
Solve each equation. Check the solution.
1. n + 6.3 = -2.5

2. 9.4 = w – 9.4

3. k – ¾ = -2/3

4. 4/5 = b – (-1/2)

5. 21/5 + p = 17/8           13/40
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
a. 2.7 + h < 3.8
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
a. 2.7 + h < 3.8
2.7 + h < 3.8
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
a. 2.7 + h < 3.8
2.7 + h < 3.8              Get h alone on one side.
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
a. 2.7 + h < 3.8
2.7 + h < 3.8              Get h alone on one side.
2.7 – 2.7+ h < 3.8 – 2.7 Subtract 2.7 from each side.
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
a. 2.7 + h < 3.8
2.7 + h < 3.8              Get h alone on one side.
2.7 – 2.7+ h < 3.8 – 2.7 Subtract 2.7 from each side.
h < 1.1
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
a. 2.7 + h < 3.8
2.7 + h < 3.8              Get h alone on one side.
2.7 – 2.7+ h < 3.8 – 2.7 Subtract 2.7 from each side.
h < 1.1

Check: Try 0, a number less than 1.1.
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
a. 2.7 + h < 3.8
2.7 + h < 3.8              Get h alone on one side.
2.7 – 2.7+ h < 3.8 – 2.7 Subtract 2.7 from each side.
h < 1.1

Check: Try 0, a number less than 1.1.
2.7 + h < 3.8
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
a. 2.7 + h < 3.8
2.7 + h < 3.8              Get h alone on one side.
2.7 – 2.7+ h < 3.8 – 2.7 Subtract 2.7 from each side.
h < 1.1

Check: Try 0, a number less than 1.1.
2.7 + h < 3.8
2.7 + 0 <? 3.8
2.7 < 3.8
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
a. 2.7 + h < 3.8
2.7 + h < 3.8              Get h alone on one side.
2.7 – 2.7+ h < 3.8 – 2.7 Subtract 2.7 from each side.
h < 1.1

Check: Try 0, a number less than 1.1.
2.7 + h < 3.8
2.7 + 0 <? 3.8
2.7 < 3.8
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
a. 2.7 + h < 3.8
2.7 + h < 3.8              Get h alone on one side.
2.7 – 2.7+ h < 3.8 – 2.7 Subtract 2.7 from each side.
h < 1.1

Check: Try 0, a number less than 1.1.
2.7 + h < 3.8
2.7 + 0 <? 3.8
2.7 < 3.8
The solution is h < 1.1, all numbers less than 1.1.
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
b. b – 1.16  5.25
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
b. b – 1.16  5.25
b – 1.16 + 1.16  5.25 + 1.16     Add 1.16 to each side.
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
b. b – 1.16  5.25
b – 1.16 + 1.16  5.25 + 1.16     Add 1.16 to each side.
b  6.41
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
b. b – 1.16  5.25
b – 1.16 + 1.16  5.25 + 1.16     Add 1.16 to each side.
b  6.41

Check: Try 7.16, a number greater than 6.41.
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
b. b – 1.16  5.25
b – 1.16 + 1.16  5.25 + 1.16     Add 1.16 to each side.
b  6.41

Check: Try 7.16, a number greater than 6.41.
b – 1.16  
716 - 116  
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
b. b – 1.16  5.25
b – 1.16 + 1.16  5.25 + 1.16     Add 1.16 to each side.
b  6.41

Check: Try 7.16, a number greater than 6.41.
b – 1.16  
716 - 116  
6  
5-7 Solving Inequalities

Example
Solve each inequality. Graph each solution on a number line.
b. b – 1.16  5.25
b – 1.16 + 1.16  5.25 + 1.16     Add 1.16 to each side.
b  6.41

Check: Try 7.16, a number greater than 6.41.
b – 1.16  
716 - 116  
6  
The solution is b  6.41, all numbers greater than or equal to 6.41.
5-7 Solving Inequalities

Assignment:12 - 28 even, 29 - 41 all

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