Question

Which equation is an identity?

7m – 5 = 8m + 7 – m


3w + 8 – w = 4w – 2(w – 4)


9 – (2v + 3) = –2v – 6


–3y + 3 = –3y – 6

Please explain your answer.

Answer 1

The equation that represents an identity is
3w + 8 – w = 4w – 2(w – 4). w = 8

Answer 2

The correct option is 2.

Explanation:

The equations that are true for any value of the variable, no matter what value is plugged in for the variable, then they are called Identity equations.

The first equation is

`7m-5=8m+7-m`

`7m-5=7m+7`

Subtract 7m from both the sides.

`-5=7`

This statement is false for any value of m. Therefore this is not an Identity equation.

The second equation is

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

Using distributive property,

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

`2w+8=2w+8`

`0=0`

This statement is true for any value of w. Therefore this is an Identity equation.

The third equation is

`9-(2v+3)=-2v-6`

`9-2v-3=-2v-6`

`-2v+6=-2v-6`

`6=-6`

This statement is false for any value of v. Therefore this is not an Identity equation.

The fourth equation is

`-3y+3=-3y-6`

Add 3y on both the sides.

`3=-6`

This statement is false for any value of y. Therefore this is not an Identity equation.

Hence the correct option is 2.