Question

Is the equation \(-2(4-x)=2 x-8\) an identity? Explain why or why not.

Short answer

No, the given equation \(-2(4-x)=2x-8\) is not an identity because the terms order are not the same on both sides.

Step-by-step solution

Simplify the left side of the equation

The left side of the equation is \(-2(4-x)\). By applying the distributive property, the equation simplifies to \(-2*4 - (-2*x)\) which equals \(-8+2x\).

Simplify the right side of the equation

The right side of the equation is \(2x - 8\). This equation is already simplified.

Compare the simplified left and right sides

After simplification, it can be seen that the left side, \(-8+2x\), matches with the right side, \(2x - 8\). However, because the term of x in the left side and right side is not the same specifically because of terms order, therefore, the equation is not an identity. Terms order is important for the expression to be an identity.