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:
[tex]\frac{1}{4} (x-2)+\frac{1}{3}x[/tex]
Then, the steps to find an equivalent expression to the given expression, are shown below:
Step 1: You must apply the Distributive property:
[tex]=(\frac{1}{4})(x)-(2)(\frac{1}{4})+\frac{1}{3}x=\frac{1}{4}x-\frac{2}{4}+\frac{1}{3}x[/tex]
Step 2: Now you need to reduce the fraction [tex]\frac{2}{4}[/tex]:
[tex]=\frac{x}{4}-\frac{1}{2}+\frac{1}{3}x[/tex]
Step 3: And finally you need to add the like terms (Notice that, in this case, the like terms are: [tex]\frac{1}{4}x[/tex] and [tex]\frac{1}{3}x[/tex]). Then, you get:
[tex]=\frac{7}{12}x-\frac{1}{2}[/tex]
