Chapter 7 Lesson 6 Solving Multi-Step Inequalities pgs. 355-359

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Chapter 7 Lesson 6Solving Multi-Step
Inequalitiespgs. 355-359

• What youll learn
• Solve inequalities that involve more than one
  operation

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Nearly 10 million Americans go backpacking each
year. According to a fitness magazine, to avoid
injury, three times the weight of your backpack
and its contents should be less than your body
weight.

• Write an inequality that represents the
  relationship between body weight and a safe total
  backpack and contents weight.
• Suppose you weigh 120 pounds and your empty
  backpack weighs 5 pounds. Write an inequality
  that represents the maximum weight you can safely
  carry in the backpack.

3(p c) ? b
3(5 c) ? 120
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Example 1 Solve a Two-Step Inequality
Some inequalities involve more than one
operation. To Solve the inequality, work
backward to undo the operations, just like you
did in solving multi-step equations.

• Solve 3x 4 ? 31 and check your solution. Graph
  the solution on a number line.

Write the inequality 3x 4
?31 Subtract 4 from each side 3x 4 -4 ? 31
-4 Simplify 3x ? 27 Divide
each side by 3 3x ? 27 3 3
Simplify x ? 9
Check in the original problem using 7 3(7) 4 ?
31 21 4 ? 31 25 ? 31 ?
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Example 2 Reverse the Inequality Symbol

• Solve -6.1n ? 3.9n 5, check your solution and
  graph the solution on a number line.

Write the inequality -6.1n ? 3.9n 5 Subtract
3.9n from each side -6.1n ? 3.9n 5
-3.9n -3.9n
Simplify -10n ? 5 Reverse the inequality and
divide each side by -10 -10n ? 5
-10 -10 Simplify n ? -0.5
Check using -1 in the original Inequality -6.1(-1
) ? 3.9(-1) 5 6.1 ? -3.9 5 6.1 ? 1.1 ?
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• Remember DO NOT reverse the inequality sign
  just because there is a negative sign in the
  inequality!!!
• Only reverse the sign when you multiply or divide
  by a negative number. (In other words, when the
  variable is negative).

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Example 3 Inequalities with grouping symbols

• A person weighing 213 pounds has a 10-pound
  backpack. Refer to the application on pg. 355 in
  the text. What is the maximum weight for the
  contents of the pack?

Words 3 times weight of pack contents
should be less than body weight Inequaltiy 3
(10 c) ? 213
Write the inequality 3 (10 c) ? 213
Distribute 30 3c ? 213 Sub. 30 from each
side 30 - 30 3c ? 213 - 30 Simplify 3c
? 183 Divide each side by 3 3c ?
183 3 3 Simplify c ? 61
So the contents Should weigh less Than 61 pounds
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Now you give it a whirl!!
Solve, check and graph each inequality
m 9 -9 ? 5 - 9 2 m ? -4
2 m ? -8 (2) m ? -4(2) 2

• m 9 ? 5
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• B. 16 - 4n ? 20
• C. 3x - 2 ?10 - x
• D. 0.5a - 1.4 ? 2.1

16 -16 - 4n ? 20 - 16 -4n ? 4
n ? -1
3x - 2 2 ? 10 2 -x 3x ?12 - x 3x x ? 12 - x
x 4x ? 12 x ? 3
.5a -1.4 1.4 ? 2.1 1.4 .5a ? 3.5 a ? 7
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• Take a look over this tonight. There will be a
  quiz tomorrow!