37 Solving Inequalities by Multiplying or Dividing

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3-7 Solving Inequalities byMultiplying or
Dividing

• Objective Solve inequalities by using the
  multiplication and division properties of
  inequalities.

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5-Minute Check

• Solve each inequality.
• r 9 lt 4

3
5-Minute Check

• Solve each inequality.
• r 9 lt 4 r lt 13

4
5-Minute Check

• Solve each inequality.
• r 9 lt 4
• s 24 gt 23

5
5-Minute Check

• Solve each inequality.
• r 9 lt 4
• s 24 gt 23 s gt -1

6
5-Minute Check

• Solve each inequality.
• r 9 lt 4
• s 24 gt 23
• t (-30) 40

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5-Minute Check

• Solve each inequality.
• r 9 lt 4
• s 24 gt 23
• t (-30) 40 t 10

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5-Minute Check

• Solve each inequality.
• r 9 lt 4
• s 24 gt 23
• t (-30) 40
• u (-14) ³ -29

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5-Minute Check

• Solve each inequality.
• r 9 lt 4
• s 24 gt 23
• t (-30) 40
• u (-14) ³ -29 u ³ -15

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5-Minute Check

• Solve each inequality.
• r 9 lt 4
• s 24 gt 23
• t (-30) 40
• u (-14) ³ -29
• 19 lt v 9

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5-Minute Check

• Solve each inequality.
• r 9 lt 4
• s 24 gt 23
• t (-30) 40
• u (-14) ³ -29
• 19 lt v 9 v gt 28

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3-7 Solving Inequalities byMultiplying or
Dividing
When you multiply or divide each side of an
inequality by a positive integer, the result
remains true.
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3-7 Solving Inequalities byMultiplying or
Dividing
Example 1 Solve 9x gt -36 and graph the solution
on a number line.
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3-7 Solving Inequalities byMultiplying or
Dividing
Example 1 Solve 9x gt -36 and graph the solution
on a number line. 9x gt -36
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3-7 Solving Inequalities byMultiplying or
Dividing
Example 1 Solve 9x gt -36 and graph the solution
on a number line. 9x gt -36
9x/9 gt -36/9 Divide each side by 9.
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3-7 Solving Inequalities byMultiplying or
Dividing
Example 1 Solve 9x gt -36 and graph the solution
on a number line. 9x gt -36
9x/9 gt -36/9 Divide each side by 9.
x gt -4
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3-7 Solving Inequalities byMultiplying or
Dividing
Example 1 Solve 9x gt -36 and graph the solution
on a number line. 9x gt -36
9x/9 gt -36/9 Divide each side by 9.
x gt -4
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3-7 Solving Inequalities byMultiplying or
Dividing
Example 2 Solve -4x ³ 12 and graph the solution
on a number line.
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3-7 Solving Inequalities byMultiplying or
Dividing
Example 2 Solve -4x ³ 12 and graph the solution
on a number line. -4x ³ 12
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3-7 Solving Inequalities byMultiplying or
Dividing
Example 2 Solve -4x ³ 12 and graph the solution
on a number line. -4x ³ 12
-4x/(-4) 12/(-4) Divide each side by 4
and reverse the order symbol.
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3-7 Solving Inequalities byMultiplying or
Dividing
Example 2 Solve -4x ³ 12 and graph the solution
on a number line. -4x ³ 12
-4x/(-4) 12/(-4) Divide each side by 4 and
x -3 reverse the order symbol.
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3-7 Solving Inequalities byMultiplying or
Dividing
Example 2 Solve -4x ³ 12 and graph the solution
on a number line. -4x ³ 12
-4x/(-4) 12/(-4) Divide each side by 4 and
x -3 reverse the order symbol.
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3-7 Solving Inequalities byMultiplying or
Dividing
Integration The area of a rectangle is at least
four times as large as its length. If its length
is 5 cm, find its width.
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3-7 Solving Inequalities byMultiplying or
Dividing
Integration The area of a rectangle is at least
four times as large as its length. If its length
is 5 cm, find its width. Answer The width
must be ³ 4 cm.
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3-7 Solving Inequalities byMultiplying or
Dividing
Assignment 16 32 even, 33 45 all, Starting
on page 154