Problem 2

Question

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

Step-by-Step Solution

Verified
Answer
Yes, the equation \(-2(4-x)=2 x-8\) is an identity as it holds true for all values of \( x \).
1Step 1: Simplify left-hand side
Start by simplifying the left-hand side of the equation, which is \( -2(4-x) \). Distributing \( -2 \) through the terms gives \( -8 + 2x \).
2Step 2: Simplify right-hand side
The right-hand side of the equation, \( 2x - 8 \), is already simplified.
3Step 3: Compare both sides
Now compare both sides of the equation to see if they are equal. Since the right-hand side \( 2x - 8 \) is equal to the left-hand side \( -8 + 2x \), the equation holds true for all values of \( x \). Therefore, the equation is an identity.