# Which is equivalent to 3/8x

 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. As I said, there are infinite fractions that equal to #3/8#. Therefore, I' m going to show you a way to get a fraction equivalent to #3/8#. Procedure/Step(s): 1) Pick a number that you want and make sure that that number is both numerator and denominator. Example: #4/4# (You don't have to pick 4/pick any number you want!) 2) Multiply the fraction that you chose with #3/8# Note: Do NOT simplify! If you do, you're just gonna get #3/8#! #3/8##times##4/4##=##12/32# So, an equivalent fraction to#3/8# is #12/32#. I hope that helps! All the best!