Question

Which equation is an identity?

3w + 8 – w = 4w – 2(w – 4)

5y + 5 = 5y – 6

6m – 6 = 7m + 9 – m

8 – (6v + 7) = –6v – 1

Answer 1

The condition for an expression to be an identity is that both sides of equality must give the same value.

In this case, the equation that fulfills that condition is the first equation (1).

Let’s prove it:

1)
`3w+8-w=4w-2(w-4)`

Applying distributive property:

`3w+8-w=4w-2w+8`

Joining together similar terms on both sides of the equality:

`2w+2w-4w=8-8`

`0=0` >>>>>>>This is true and fulfills the condition of identity

The other equations do not fulfill the condition:

2)
`5y+5=5y-6`

`5y-5y=-6-5`

`0 =-11` >>>>>>>This is not logic

3)
`6m-6=7m+9-m`

`6m-7m+m=9+6`

`0=15` >>>>>>>This is not logic

4)
`8-(6v+7)=-6v-1`

`8-6v-7=-6v-1`

`1=-1` >>>>>>>This is not logic