Question

Is the equation
`-2(4-x)=2x+8` an identity? Explain your reasoning.

A. Yes, because solving the equation gives a statement that is never true.

B. Yes, because solving the equation gives a statement that is always true.

C. No, because solving the equation gives a statement that is never true.

D. No, because solving the equation gives a statement that is always true.


help I don't know what an identity is or how to explain

Answer 1

Given:

The equation is
`-2(4-x)=2x+8`.

To find:

Whether the given equation is an identity or not.

Solution:

If both sides of an equation are equal for all values of variables, then it is called identity.

We have,

`-2(4-x)=2x+8`

`LHS=-2(4-x)`

`LHS=-2(4)-2(-x)`

`LHS=-8+2x`

`LHS=2x-8`

Now,

`2x-8=2x+8`

On subtracting 2x from both sides, we get

`-8=8`

This statement is never true.

`LHS\\eq RHS`

So, the given equation is not an identity because solving the equation gives a statement that is never true.

Therefore, the correct option is C.