Solving Inequalities

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# Solving Inequalities - PowerPoint PPT Presentation

Solving Inequalities. Section 1.4. Check Skills You’ll Need. Work problems 1-8 on page 26 in your textbook. Answers:. In this lesson you will. Solve and graph inequalities Solve and write compound inequalities. Solving and Graphing Inequalities. Solve -2x &lt; 3(x – 5). Graph the solution.

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### Solving Inequalities

Section 1.4

Check Skills You’ll Need
• Work problems 1-8 on page 26 in your textbook.
In this lesson you will
• Solve and graph inequalities
• Solve and write compound inequalities
Solving and Graphing Inequalities
• Solve -2x < 3(x – 5). Graph the solution.
Check Understanding
• Solve each inequality and graph the solution.
Example 2
• Solve 7x ≥ 7(2 + x)
Check Understanding
• Solve each inequality and graph the solution.
• If an inequality is always false, it has no solution. 0 < -7
• If an inequality is always true, then all real numbers are solutions. 3 > 0

-2 -1 0 1 2

Check Understanding

All real numbers are solutions.

Check Understanding

This inequality has no solution.

-1

3

Compound Inequalities
• Graph the solution of 2x – 1 ≤ 3x and x > 4x – 9.
Check Understanding
• Graph the solution of the compound inequality

6

9

Compound Inequalities Containing OR
• Graph the solution of 3x + 9 < -3 or -2x + 1 < 5

-4

-2

Check Understanding
• Solve the compound inequality and graph the solution.

4

5

Applying Compound Inequalities
• A strip of wood is to be 17 cm long with a tolerance of ±0.15 cm. How much should be trimmed from a strip 18 cm long to allow it to meet specifications?

Mimimum length

Final length

Maximum length

Let x be the number of centimeters to remove.

16.85

16.85

16.85

18 - x

18 - x

18 - x

17.15

17.15

17.15

Now solve for x.

16.85

18 - x

17.15

Subtract 18

Multiply by -1

At least .85 cm and no more than 1.15 cm should be trimmed.

Mimimum diameter

Final length

Maximum diameter

Check Understanding
• Now work the problem on page 29 of your textbook.

Let x be the number of inches to remove

The diameter should be decreased by at least 0.03 in and no more than 0.43 in.