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Question 99293: how do i figure out 2(x+4)-5(x-3)=32
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
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2(x+4)-5(x-3)=32
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The first thing to do is the two distributed multiplications on the left side of this equation.
Multiply the 2 times each of the two terms in its set of parentheses. When you do that you
are multiplying 2 times x and then adding to that 2 times +4. This makes the first distributed
multiplication become 2x + 8.
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Then do the distributed multiplication of -5 times each of the two terms inside its corresponding
set of parentheses. So you are multiplying -5 times x to get -5x and then you are multiplying
-5 times -3 to get +15. So the result of this multiplication is -5x + 15.
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Substitute these two results for the distributed multiplications you were given and the
left side of the equation changes in the equation as follows:
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2x + 8 - 5x + 15 = 32
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On the left side combine the -5x and the +2x to get -3x and the equation becomes:
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-3x + 8 + 15 = 32
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Then on the left side combine the +8 and +15 to get +23. This simplifies the equation to:
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-3x + 23 = 32
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Get rid of the +23 on the left side by subtracting 23 from both sides to make the equation:
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-3x = +9
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Finally solve for x by dividing both sides of the equation by -3 to get:
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x = 9/(-3) = -3
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So x = -3 is the answer.
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Check by returning to the given equation and substituting -3 for x to see if the left side
of the equation will equal the right side. So start with:
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2(x+4)-5(x-3)=32
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Substitute -3 for x and this equation becomes:
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2(-3+4) -5(-3-3)= 32
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combine the numbers in the parentheses and the equation becomes:
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2(1) - 5(-6) = 32
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Multiply 2 times 1 to get 2 and multiply -5 times -6 to get +30. This makes the equation:
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2 + 30 = 32
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That is a correct equality. So x = -3 checks out OK . The answer to this problem is
x = -3.
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Hope this helps you to understand the problem and how to work it to get the answer.
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