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Question 1027608: What is the answer to this question?
Determine which expression is equivalent to 3/4-x(1/2-5/8)+(-3/8x)
A. -3/4x
B. 1/2x
C. 1/8-7/8x
D. 3/4-1/4x
So I did try to simplify the expression and got 3/4-x(-1/8)+(-3/8x). I don't know what to do now?! Please help!
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20849)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! looking at where you got to and got stuck, let's see what we can do, if anything, to further simplify it.
the original expression is:
3/4-x(1/2-5/8)+(-3/8x)
you got:
3/4-x(-1/8)+(-3/8x)
looks like you were able to simplify (1/2 - 5/8) correctly.
to simplify further, you have to perform the operations indicated.
+(-3/8x) is equivalent to -3/8x
-x(-1/8) is equivalent to 1/8x.
the expression becomes 3/4 + 1/8x - 3/8x
1/8x - 3/8x is equal to -2/8x
the expression becomes 3/4 - 2/8x
2/8x is equivalent to 1/4x
the expression becomes 3/4 - 1/4x
that looks like selection D.
sometimes it's helpful to insert the operational symbols where they are implied.
that makes it easier to analyze.
your original expression was, once again:
3/4-x(1/2-5/8)+(-3/8x)
after insertion of implied operational symbols, the expression becomes:
3/4 - x * (1/2 - 5/8) + (-3/8 * x)
your original simplification was correct, so we'll go with that to get:
3/4 - x * (-1/8) + (-3/8 * x)
x * (-1/8) is equivalent to -1/8 * x, so the expression becomes:
3/4 - (-1/8) * x + (-3/8 * x)
since multiplying a negative by another negative results in a positive, the expression becomes:
3/4 + 1/8 * x + (-3/8 * x)
since adding a negative is the same as subtracting a positive, the expression becomes:
3/4 + 1/8 * x - 3/8 * x
you combine like terms by taking + 1/8 * x - 3/8 * x and combining them to get -2/8 * x.
the expression becomes 3/4 - 2/8 * x.
since 2/8 * x can be simplified to -1/4 * x, the final expression becomes:
3/4 - 1/4 * x.
this is the same as 3/4 - 1/4x shown in selection D.
one way to confirm you did the simplification correctly is to assign a random value to x and evaluate the original expression and the final expression using that value.
if the result is the same, then you simplified correctly.
i chose x = 13 at random.
you can use your calculator for this to avoid unnecessary extra work in resolving fractions.
i used my calculator after assigning the value of 13 to x and i got:
the original expression of 3/4-x(1/2-5/8)+(-3/8x) = -2.5
the final expression of 3/4 - 1/4 * x = -2.5
the result was the same so i can assume my simplification is correct.
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