Question

Is the equation align="absmiddle" class="latex-formula"> 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.

$LHS\neq RHS$

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.