Solving Inequalities

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Solving Inequalities

• Section 1.4

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Check Skills Youll Need

• Work problems 1-8 on page 26 in your textbook.
• Answers

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In this lesson you will

• Solve and graph inequalities
• Solve and write compound inequalities

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Solving and Graphing Inequalities

• Solve -2x lt 3(x 5). Graph the solution.

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Check Understanding

• Solve each inequality and graph the solution.

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Example 2

• Solve 7x 7(2 x)

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Check Understanding

• Solve each inequality and graph the solution.

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Inequalities with No Solution or All Real Numbers
as Solutions

• If an inequality is always false, it has no
  solution. 0 lt -7
• If an inequality is always true, then all real
  numbers are solutions. 3 gt 0

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Check Understanding
All real numbers are solutions.
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Check Understanding
This inequality has no solution.
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Compound Inequalities

• Graph the solution of
  2x 1 3x and x gt 4x 9.

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Check Understanding

• Graph the solution of the compound inequality

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9
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Compound Inequalities Containing OR

• Graph the solution of
  3x 9 lt -3 or -2x 1 lt
  5

-4
-2
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Check Understanding

• Solve the compound inequality and graph the
  solution.

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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.
18 - x


16.85
17.15
18 - x


16.85
17.15
18 - x


16.85
17.15
Now solve for x.
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Subtract 18
Multiply by -1
At least .85 cm and no more than 1.15 cm should
be trimmed.
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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.