Question

Use properties to rewrite the given equation. Which equations have the same solution as the equation

x + + x = – x plus StartFraction 2 Over 3 EndFraction plus x equals StartFraction one-half EndFraction minus StartFraction 1 Over 5 EndFraction x.x

Select three options.

x + StartFraction 8 Over 5 EndFraction x plus StartFraction 2 Over 3 EndFraction equals StartFraction one-half EndFraction minus StartFraction 1 Over 5 EndFraction x. = – x plus StartFraction 2 Over 3 EndFraction plus x equals StartFraction one-half EndFraction minus StartFraction 1 Over 5 EndFraction x.x
18x + 20 + 30x = 15 – 6x
18x + 20 + x = 15 – 6x
24x + 30x = –5
12x + 30x = –5

Answer 1

I can’t reliably pick the three correct choices because the equation and the answer choices are garbled. Could you retype the original equation and the full list of choices using plain text (for example: -x + 2/3 + x = 1/2 - (1/5)x and choices like 20 = 15 - 6x)?

If the equation is
-x + 2/3 + x = 1/2 - (1/5)x
then it simplifies to
2/3 = 1/2 - (1/5)x.
Multiplying both sides by 30 gives
20 = 15 - 6x,
which is equivalent to
6x = -5 (and therefore x = -5/6).
Any equivalent choice must be one of these forms (or a nonzero multiple of both sides), e.g. 20 = 15 - 6x, 6x = -5, 12x = -10, 18x = -15, etc.

If you paste the exact choices I’ll mark which three match.