Question 73252
{{{abs(x+2) = 3}}}
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You have both answers correct.  Here's one way that you can do the math. It involves
solving two equations.
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Begin by pulling the quantity out of the absolute value signs.  In this problem that quantity
is (x+2).
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For the first equation set up and solve the problem with a plus sign in front of the quantity:
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{{{+(x+2) = 3}}}
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Since the parentheses are preceded by a plus sign, you can just remove them and the equation
becomes:
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{{{x+2 = 3}}}
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Subtract 2 from both sides of this equation to eliminate the 2 on the left side and the
equation is then:
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{{{x = 1}}}
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This is one of the answers you are looking for.
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Now recall that near the start we set up the equation with a plus sign in front of the quantity.
Well, let's do that again EXCEPT this time we'll put a minus sign in front of the quantity.
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{{{-(x+2) = 3}}}
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When you remove the parentheses this time the minus sign in front of them makes it necessary
to change the sign of everything inside the parentheses.  [In effect you are multiplying
the quantity by minus 1.] So the resulting equation is:
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{{{-x-2 = 3}}}
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Add 2 to both sides of the equation to eliminate the -2 on the left side.  Adding this 2
makes the equation become:
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{{{-x = 5}}}
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To solve for x just multiply both sides of the equation by -1 to get:
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{{{x = -5}}}
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Now you have both answers.  One of the answers is x = 1 and the other answer is x = -5.
The graph of these two answers is the number line with dots at +1 and -5 as shown below:
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{{{number_line(600,-10,10,-5,+1)}}}
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I hope this method makes it easier for you to work these problems.