Question

Which expression is equivalent to the expression 1/4 (x-2) + 1/3x?

Answer 1

Answer: First option.

Step-by-step explanation:

By definition, equivalent expressions have the same value but they look different.

The exercise gives the following expression:

$\frac{1}{4} (x-2)+\frac{1}{3}x$

Then, the steps to find an equivalent expression to the given expression, are shown below:

Step 1: You must apply the Distributive property:

$=(\frac{1}{4})(x)-(2)(\frac{1}{4})+\frac{1}{3}x=\frac{1}{4}x-\frac{2}{4}+\frac{1}{3}x$

Step 2: Now you need to reduce the fraction $\frac{2}{4}$:

$=\frac{x}{4}-\frac{1}{2}+\frac{1}{3}x$

Step 3: And finally you need to add the like terms (Notice that, in this case, the like terms are: $\frac{1}{4}x$ and $\frac{1}{3}x$). Then, you get:

$=\frac{7}{12}x-\frac{1}{2}$