Question

1. select all expressions equivalent to $-\frac{2}{3}x + 2$.

$ -2 - \frac{2}{3}x $
$ 2 - \frac{2}{3}x $
$ -1 - \frac{2}{3}x + 1 $
$ -\frac{1}{3}x - 4 + 2 $
$ -\frac{2}{3}x - 3 + 5 $

Explanation:

Step1: Analyze the first option

The given expression is $-\frac{2}{3}x + 2$. The first option is $-2-\frac{2}{3}x$, which has a constant term of -2 instead of 2, so it's not equivalent.

Step2: Analyze the second option

The second option is $2-\frac{2}{3}x$, which is the same as $-\frac{2}{3}x + 2$ (by the commutative property of addition), so this is equivalent.

Step3: Analyze the third option

Simplify the third option: $-1-\frac{2}{3}x + 1$. Combine the constant terms: $(-1 + 1)-\frac{2}{3}x = 0-\frac{2}{3}x=-\frac{2}{3}x$, which is not equivalent to $-\frac{2}{3}x + 2$.

Step4: Analyze the fourth option

Simplify the fourth option: $-\frac{1}{3}x-4 + 2=-\frac{1}{3}x-2$, which has a different coefficient for $x$ and a different constant term, so it's not equivalent.

Step5: Analyze the fifth option

Simplify the fifth option: $-\frac{2}{3}x-3 + 5$. Combine the constant terms: $-\frac{2}{3}x+( - 3 + 5)=-\frac{2}{3}x + 2$, so this is equivalent.

Answer:

The equivalent expressions are:

• $2-\frac{2}{3}x$
• $-\frac{2}{3}x - 3 + 5$