SOLUTION: how do i figure out 2(x+4)-5(x-3)=32

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:
.
2(x+4)-5(x-3)=32
.
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.
.
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.
.
Substitute these two results for the distributed multiplications you were given and the
left side of the equation changes in the equation as follows:
.
2x + 8 - 5x + 15 = 32
.
On the left side combine the -5x and the +2x to get -3x and the equation becomes:
.
-3x + 8 + 15 = 32
.
Then on the left side combine the +8 and +15 to get +23. This simplifies the equation to:
.
-3x + 23 = 32
.
Get rid of the +23 on the left side by subtracting 23 from both sides to make the equation:
.
-3x = +9
.
Finally solve for x by dividing both sides of the equation by -3 to get:
.
x = 9/(-3) = -3
.
So x = -3 is the answer.
.
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:
.
2(x+4)-5(x-3)=32
.
Substitute -3 for x and this equation becomes:
.
2(-3+4) -5(-3-3)= 32
.
combine the numbers in the parentheses and the equation becomes:
.
2(1) - 5(-6) = 32
.
Multiply 2 times 1 to get 2 and multiply -5 times -6 to get +30. This makes the equation:
.
2 + 30 = 32
.
That is a correct equality. So x = -3 checks out OK . The answer to this problem is
x = -3.
.
Hope this helps you to understand the problem and how to work it to get the answer.
.
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