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Question 74808This question is from textbook Algebra I
:
solve the inequality
8c-(c-5)>c+17
This question is from textbook Algebra I
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 8c-(c-5)>c+17
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You can perform math operations on inequalities just as you would on an equation with the
exception that if in solving this problem you need to multiply or divide both sides by
a negative quantity, you must reverse the direction of the inequality sign.
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Let's work this problem just as we would an equation. The goal is to get the variable c
on one side of the inequality and the numbers on the other side.
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Begin by removing the parentheses. Since the parentheses are preceded by a negative
sign, you can remove the parentheses as long as you change the signs of the terms inside them.
Applying this rule results in:
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8c - c + 5 > c + 17
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On the left side, combine the two terms containing c to get:
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7c + 5 > c + 17
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Get rid of the c on the right side by subtracting c from both sides to get:
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6c + 5 > 17
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Get rid of the +5 on the left side by subtracting 5 from both sides:
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6c > 12
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Solve for c by dividing both sides by 6 the multiplier of c:
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c > 2
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That's the answer. The original inequality will hold for all values of c that are greater
than +2.
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Notice we did not need to apply the rule that if you divide or multiply both sides by
a negative number you need to reverse the direction of the inequality sign.
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Hope this clarifies the problem for you and helps you to see how to solve inequalities.
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