Question

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

7/12x - 1/2

7/12x-2

-1/12x-1/2

-1/12x-2

Answer 1

Answer: First option.

Explanation:

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

The exercise gives the following expression:

`(1)/(4) (x-2)+(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:

`=((1)/(4))(x)-(2)((1)/(4))+(1)/(3)x=(1)/(4)x-(2)/(4)+(1)/(3)x`

Step 2: Now you need to reduce the fraction
`(2)/(4)`:

`=(x)/(4)-(1)/(2)+(1)/(3)x`

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

`=(7)/(12)x-(1)/(2)`