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

Responses

x=2
x equals 2

no solution
no solution

x=−3
x equals negative 3

x=0

1 answer

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.