Question

Determine whether the equation below is an identity or whether it has no solution.
negative 3 left parenthesis 2 x plus 2 right parenthesis equals negative 6 x minus 6
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Part 1
Choose the correct answer below.
The equation is an identity.
The equation has no solution.

Answer 1

To determine if the equation \(-3(2x + 2) = -6x - 6\) is an identity or if it has no solution, we can simplify both sides.

1. Start with the left side:
\[
-3(2x + 2) = -3 \cdot 2x - 3 \cdot 2 = -6x - 6
\]

2. The right side is already:
\[
-6x - 6
\]

Now, we compare the simplified left and right sides:
- Left side: \(-6x - 6\)
- Right side: \(-6x - 6\)

Since both sides of the equation are equal, this equation holds true for all values of \(x\). Thus, the equation is an identity.

The correct answer is:
**The equation is an identity.**