You can put this solution on YOUR website! Given:
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You want to isolate the absolute value quantity on one side of the equation and get everything
else on the other side. Start by subtracting 3 from both sides to remove it from the left
side. When you subtract 3 from both sides the result is:
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Next you can get rid of the -(1/2) in front of the absolute value sign by multiplying both
sides of this equation by -2. This multiplication results in the equation becoming:
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You can now remove the absolute value signs if you set up two separate equations to be solved.
First, take the quantity inside the absolute value signs, preface it by a plus sign, and
set it equal to the right side. Then solve this equation for x. That will be one solution.
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Second, take the quantity inside the absolute value signs, preface it by a minus sign, and
set it equal to the right side. Then solve this equation for x. That will be the second
solution.
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Let's do the first case. The quantity inside the absolute value sign is:
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and since it is preceded by a plus sign, it is not changed. Set it equal to the right side
which is and the equation to solve becomes:
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Add 4 to both sides of this equation to get rid of the -4 on the left side and you get:
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Then multiply both sides by 2 and the equation becomes:
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That's one solution. Now let's go to the second case. Take the quantity inside the absolute
value signs and precede it by a minus sign. Then set it equal to 2 also. This equation is:
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The minus sign tells you to change the signs of the terms inside the parentheses.
When you do that the equation becomes:
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Subtract +4 from both sides of the equation to get rid of the 4 on the left side. This
subtraction makes the equation become:
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Solve for x by multiplying both sides of this equation by -2 to get:
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And that's the second answer. So the two answers to this problem are x = +4 and x = +12
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You can check both these answers by substituting the for x (one at a time) into the original
given problem and you will find that they both make the left side of the given problem
equal the right side.
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Hope this procedure of taking the quantity inside the absolute value signs and first
assigning it a + sign and setting it equal to the right side and then assigning it a - sign
and setting it equal to the right side helps you to find the answers to absolute value problems
of this type. It makes it easier because it gets rid of the absolute value signs and
just results in two equations to solve using your regular equation solving skills.
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