Question

Which equation is an identity?

3w + 8 – w = 4w – 2(w – 4)


–3y + 3 = –3y – 6


9 – (2v + 3) = –2v – 6


7m – 5 = 8m + 7 – m

Answer 1

3w + 8 – w = 4w – 2(w – 4)

Explanation:

`3w+8-w=4w-2(w-4)\qquad\text{use the distributive property}\\\\2w+8=4w-2w+8\\\\2w+8=2w+8\qquad\text{subtract}\ 2m\ \text{from both sides}\\\\8=8\qquad\bold{TRUE}`

`-3y+3=-3y-6\qquad\text{add}\ 3y\ \text{to both sides}\\\\3=-6\qquad\bold{FALSE}\\\\9-(2v+3)=-2v-6\\\\9-2v-3=-2v-6\qquad\text{add}\ 2v\ \text{to both sides}\\\\6=-6\qquad\bold{FALSE}\\\\7m-5=8m+7-m\\\\7m-5=7m+7\qquad\text{subtract}\ 7m\ \text{from both sides}\\\\-5=7\qquad\bold{FALSE}`