Solve the absolute value equation −3−|6−3x|+7=4 .(1 point) Responses no solution no solution x=−3 x equals negative 3 x=0 x equals 0 x=2

Answer 1

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

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

This simplifies to:

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

Subtracting 4 from both sides gives us:

\[

• |6 - 3x| = 0 \]

Multiplying through by -1, we have:

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

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

\[ 6 - 3x = 0 \]

Next, we solve for \(x\):

\[ 3x = 6 \] \[ x = 2 \]

Thus, the solution to the equation is:

\[ \boxed{2} \]

Among the options provided, "x=2" is the correct response.