76 Solving MultiStep Inequalities

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7-6 Solving Multi-Step Inequalities

• Objective Solve inequalities that involve more
  than one operation.

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5-Minute Check

• Solve each equation.
• 5a 18 3a 9
• -3b 13 -b 3 8
• 4(2x 1) 3 5(x 5) -6
• 7(y 3) 2 3(2y 5) 4 12
• 4/7m 5 2/7m 3 -28

3
5-Minute Check

• Solve each equation.
• 5a 18 3a 9
• -3b 13 -b 3 8
• 4(2x 1) 3 5(x 5) -6
• 7(y 3) 2 3(2y 5) 4 12
• 4/7m 5 2/7m 3 -28

4
5-Minute Check

• Solve each equation.
• 5a 18 3a 9
• -3b 13 -b 3 8
• 4(2x 1) 3 5(x 5) -6
• 7(y 3) 2 3(2y 5) 4 12
• 4/7m 5 2/7m 3 -28

5
5-Minute Check

• Solve each equation.
• 5a 18 3a 9
• -3b 13 -b 3 8
• 4(2x 1) 3 5(x 5) -6
• 7(y 3) 2 3(2y 5) 4 12
• 4/7m 5 2/7m 3 -28

6
5-Minute Check

• Solve each equation.
• 5a 18 3a 9
• -3b 13 -b 3 8
• 4(2x 1) 3 5(x 5) -6
• 7(y 3) 2 3(2y 5) 4 12
• 4/7m 5 2/7m 3 -28

7
5-Minute Check

• Solve each equation.
• 5a 18 3a 9
• -3b 13 -b 3 8
• 4(2x 1) 3 5(x 5) -6
• 7(y 3) 2 3(2y 5) 4 12
• 4/7m 5 2/7m 3 -28

8
5-Minute Check

• Solve each equation.
• 5a 18 3a 9
• -3b 13 -b 3 8
• 4(2x 1) 3 5(x 5) -6
• 7(y 3) 2 3(2y 5) 4 12
• 4/7m 5 2/7m 3 -28

9
5-Minute Check

• Solve each equation.
• 5a 18 3a 9
• -3b 13 -b 3 8
• 4(2x 1) 3 5(x 5) -6
• 7(y 3) 2 3(2y 5) 4 12
• 4/7m 5 2/7m 3 -28

10
5-Minute Check

• Solve each equation.
• 5a 18 3a 9
• -3b 13 -b 3 8
• 4(2x 1) 3 5(x 5) -6
• 7(y 3) 2 3(2y 5) 4 12
• 4/7m 5 2/7m 3 -28

11
5-Minute Check

• Solve each equation.
• 5a 18 3a 9
• -3b 13 -b 3 8
• 4(2x 1) 3 5(x 5) -6
• 7(y 3) 2 3(2y 5) 4 12
• 4/7m 5 2/7m 3 -28

12
7-6 Solving Multi-Step Inequalities
Rule If each side of an inequality is multiplied
or divided by a negative number, the order symbol
of the inequality must be reversed.
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7-6 Solving Multi-Step Inequalities
Example Solve b 8 ³ 3b 8 and check the
solution. Graph the solution on a number line.
b 8 ³ 3b 8
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7-6 Solving Multi-Step Inequalities
Example Solve b 8 ³ 3b 8 and check the
solution. Graph the solution on a number line.
b 8 ³ 3b 8 b 8 8 ³ 3b 8 8
Add 8 to each side.
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7-6 Solving Multi-Step Inequalities
Example Solve b 8 ³ 3b 8 and check the
solution. Graph the solution on a number line.
b 8 ³ 3b 8 b 8 8 ³ 3b 8 8 b
3b ³ 3b 3b
Add 8 to each side. Subtract 3b from each side.
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7-6 Solving Multi-Step Inequalities
Example Solve b 8 ³ 3b 8 and check the
solution. Graph the solution on a number line.
b 8 ³ 3b 8 b 8 8 ³ 3b 8 8 b
3b ³ 3b 3b 2b 0 -2 -2
Add 8 to each side. Subtract 3b from each
side. Divide each side by 2 And change ³ to .
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7-6 Solving Multi-Step Inequalities
Example Solve b 8 ³ 3b 8 and check the
solution. Graph the solution on a number line.
b 8 ³ 3b 8 b 8 8 ³ 3b 8 8 b
3b ³ 3b 3b 2b 0 -2 -2 b
0 Any number less than or equal to zero is a
solution.
Add 8 to each side. Subtract 3b from each
side. Divide each side by 2 And change ³ to .
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7-6 Solving Multi-Step Inequalities
Check Try 1, a number less than 0. b 8 ³ 3b
8 -1 8 ³ 3(-1) 8 Replace b with 1. 9 ³
3 8 9 ³ 11
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7-6 Solving Multi-Step Inequalities
Integration In geometry, suppose that the
perimeter of a rectangle is to be at least 256 m.
If the length is three times the width, how long
will the length and width be?
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7-6 Solving Multi-Step Inequalities
Assignment 12 30 even, 31 39 all.