Question

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

x=0
𝑥
=
0
x equals 0

no solution
no solution

x=−3
𝑥
=
−
3
x equals negative 3

x=2

Answer 1

To solve the equation \(-3 - |6 - 3x| + 7 = 4\), we can first simplify it.

Starting with:

\[
-3 - |6 - 3x| + 7 = 4
\]

Combine the constants \(-3\) and \(7\):

\[
4 - |6 - 3x| = 4
\]

Next, subtract \(4\) from both sides:

\[
- |6 - 3x| = 0
\]

From this, we see that:

\[
|6 - 3x| = 0
\]

The absolute value of an expression is equal to zero only when the expression itself is equal to zero. Therefore, we set the inside of the absolute value equal to zero:

\[
6 - 3x = 0
\]

Now, we solve for \(x\):

\[
3x = 6
\]

\[
x = 2
\]

Thus, the solution to the equation is:

\[
\boxed{x = 2}
\]