Question 80743: Which of the following is the solution set of
|3x+ 18|=12
A. (2) B. (2,10) C.(-10, -2) D.(10) Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Given:
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What is the solution set?
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Work this as two separate problems. For the first problem, replace the absolute value signs
with parentheses that are preceded by a + sign. For the second problem, replace the absolute
value signs with parentheses that are preceded by a - sign. Let's do it.
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First problem. Replacing the absolute value signs by parentheses preceded by a + sign results
in:
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+(3x + 18) = 12
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Since the leading sign preceding the parentheses is + you can just remove the parentheses
and you get:
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3x + 18 = 12
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Solve by subtracting 18 from both sides and you have:
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3x = -6
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Divide by 3 and you get:
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x = -6/3 = -2
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Second problem. Replace the absolute value signs by parentheses preceded by a minus sign
and you get:
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-(3x + 18) = 12
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This time when you remove the parentheses, the leading minus sign requires that you change
the sign of all the terms inside the parentheses. When you remove the parentheses
you get:
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-3x - 18 = 12
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Get rid of the - 18 on the left side by adding + 18 to both sides to get:
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-3x = 30
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Solve by dividing both sides by -3 and you get:
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x = 30/(-3) = -10
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Check your two answers by putting them into the given absolute value equation. First check
the -2 answer.
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the 3*(-2) equals -6 and substituting this -6 results in:
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combining the terms in the absolute value signs gives you:
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and since is +12, this equation works.
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Next substitute -10 for x and you get:
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Do the multiplication in the parentheses to get:
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combine the terms in the absolute value signs to get:
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And the absolute value of -12 is +12 so the equation becomes:
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So this answer checks also.
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Another way you could have considered doing this problem is to substitute each of the
given answers into the original equation to see if it works. For example, Answer A is 2.
Substitute 2 for x in the original problem and you get:
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this simplifies to:
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and this further simplifies to:
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This is obviously wrong so A cannot be the answer. And if you do a similar process for
answers B and D you will see they do not work either. Sometimes on the ACT and SAT exams
this method will save time. Just check the answers until you find the one that works.
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Hope this helps you to understand a method for doing absolute value problems.
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