Question

determine which expressions are equivalent4-6x=2(2-3x)6-9x=3(2+3x)12-8x=-4(3+2x)10-5x=2(5+2x)

Answer 1

We have to evaluate each expression to find if the equality stands or not.

a)

$\begin{gathered} 4-6x=2(2-3x) \\ 4-6x=2\cdot2-2\cdot3x \\ 4-6x=4-6x \end{gathered}$

This expression is equivalent.

b)

$\begin{gathered} 6-9x=3(2+3x) \\ 6-9x\ne6+9x \end{gathered}$

The expressions are not equivalent, although they have a solution for x.

(Note: equivalent expression would give infinite solutions for x).

c)

$\begin{gathered} 12-8x=-4(3+2x) \\ 12-8x\ne-12+8x \end{gathered}$

The expressions are not equivalent,.

d)

$\begin{gathered} 10-5x=2(5+2x) \\ 10-5x\ne10+4x \end{gathered}$

Answer: the only pair of expressions that are equivalent are 4-6x=2(2-3x).