To solve the equation \(-3 - |6 - 3x| + 7 = 4\), first, simplify the left-hand side:
\[-3 + 7 - |6 - 3x| = 4\]
This simplifies to:
\[4 - |6 - 3x| = 4\]
Next, isolate the absolute value term:
\[-|6 - 3x| = 4 - 4\] \[-|6 - 3x| = 0\]
This implies:
\[|6 - 3x| = 0\]
The absolute value of a number is zero only when the number itself is zero, so we set the inside of the absolute value to zero:
\[6 - 3x = 0\]
Now, solve for \(x\):
\[-3x = -6\] \[x = 2\]
Thus, the solution to the equation is:
\[x = 2\]
The correct response is:
x equals 2.