Question

Solve the absolute value equation −3−|6−3x|+7=4
.(1 point)
Responses

no solution
no solution

x=−3
x equals negative 3

x=2
x equals 2

x=0

Answer 1

To solve the equation \(-3 - |6 - 3x| + 7 = 4\), we can start by simplifying it:

1. Combine the constants on the left side:
\[
-3 + 7 = 4
\]
So the equation simplifies to:
\[
4 - |6 - 3x| = 4
\]

2. Next, subtract 4 from both sides:
\[
-|6 - 3x| = 0
\]

3. Multiply both sides by -1:
\[
|6 - 3x| = 0
\]

4. The absolute value of an expression equals zero only when the expression itself is zero:
\[
6 - 3x = 0
\]

5. Now solve for \(x\):
\[
3x = 6 \\
x = 2
\]

Thus, the solution to the equation \(-3 - |6 - 3x| + 7 = 4\) is:
\[
\boxed{x = 2}
\]

Therefore, the correct response is:
x = 2.