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

Responses

x=−3
x equals negative 3

x=2
x equals 2

x=0
x equals 0

no solution
no solution

1 answer

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

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

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

  3. Multiply both sides by -1 (this reverses the inequality): \[ |6 - 3x| = 0 \]

  4. Since the absolute value of something is zero only when that something is zero, we set the inside of the absolute value to zero: \[ 6 - 3x = 0 \]

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

The solution to the equation is \( x = 2 \).

So the correct response is: x=2 (or x equals 2).