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5-7 Solving Inequalities

Objective: Solve inequalities with

rational numbers.

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5-Minute Check

Solve each equation. Check the solution.

1. n + 6.3 = -2.5

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5-Minute Check

Solve each equation. Check the solution.

1. n + 6.3 = -2.5 -8.8

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5-Minute Check

Solve each equation. Check the solution.

1. n + 6.3 = -2.5

2. 9.4 = w9.4 18.8

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5-Minute Check

Solve each equation. Check the solution.

1. n + 6.3 = -2.5

2. 9.4 = w9.4

3. k = -2/3

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5-Minute Check

Solve each equation. Check the solution.

1. n + 6.3 = -2.5

2. 9.4 = w9.4

3. k = -2/3 1/12

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5-Minute Check

Solve each equation. Check the solution.

1. n + 6.3 = -2.5

2. 9.4 = w9.4

3. k = -2/3

4. 4/5 = b(-1/2)

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5-Minute Check

Solve each equation. Check the solution.

1. n + 6.3 = -2.5

2. 9.4 = w9.4

3. k = -2/3

4. 4/5 = b(-1/2) 3/10

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5-Minute Check

Solve each equation. Check the solution.

1. n + 6.3 = -2.5

2. 9.4 = w9.4

3. k = -2/3

4. 4/5 = b(-1/2)

5. 21/5+ p = 17/8

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5-Minute Check

Solve each equation. Check the solution.

1. n + 6.3 = -2.5

2. 9.4 = w9.4

3. k = -2/3

4. 4/5 = b(-1/2)

5. 21/5+ p = 17/8 13/40

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5-7 Solving Inequalities

Example

Solve each inequality. Graph each solution on a number line.

a. 2.7 + h < 3.8

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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

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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.

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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.2.72.7+ h < 3.8 2.7 Subtract 2.7 from each side.

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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.2.72.7+ h < 3.8 2.7 Subtract 2.7 from each side.

h < 1.1

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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.2.72.7+ h < 3.8 2.7 Subtract 2.7 from each side.

h < 1.1

Check: Try 0, a number less than 1.1.

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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.2.72.7+ 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

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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.2.72.7+ 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

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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.2.72.7+ 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

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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.2.72.7+ 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

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5-7 Solving Inequalities

Example

Solve each inequality. Graph each solution on a number line.

b. b1.16 5.25

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5-7 Solving Inequalities

Example

Solve each inequality. Graph each solution on a number line.

b. b1.16 5.25

b

1.16 + 1.16 5.25 + 1.16 Add 1.16 to each side.

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5-7 Solving Inequalities

Example

Solve each inequality. Graph each solution on a number line.

b. b1.16 5.25

b

1.16 + 1.16 5.25 + 1.16 Add 1.16 to each side.b 6.41

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5-7 Solving Inequalities

Example

Solve each inequality. Graph each solution on a number line.

b. b1.16 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.

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5-7 Solving Inequalities

Example

Solve each inequality. Graph each solution on a number line.

b. b1.16 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.

b1.16

716 - 116

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5-7 Solving Inequalities

Example

Solve each inequality. Graph each solution on a number line.

b. b1.16 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.

b1.16

716 - 116

6

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5-7 Solving Inequalities

Example

Solve each inequality. Graph each solution on a number line.

b. b1.16 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.

b1.16

716 - 116

6

The solution is b 6.41, all numbers greater than or equal to 6.41.

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5-7 Solving Inequalities

Assignment:12 - 28 even, 29 - 41 all