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5. (2 points)

Solve using inverse operations. Use the sketch pad to show your work:

4(x-4)=x-13

MUST show your work.

1 answer

To solve the equation \(4(x - 4) = x - 13\) using inverse operations, follow these steps:

  1. Distribute the 4: \[ 4(x - 4) = 4x - 16 \] So the equation becomes: \[ 4x - 16 = x - 13 \]

  2. Isolate the variable term: To do this, subtract \(x\) from both sides: \[ 4x - x - 16 = -13 \] This simplifies to: \[ 3x - 16 = -13 \]

  3. Add 16 to both sides: \[ 3x - 16 + 16 = -13 + 16 \] Simplifying gives: \[ 3x = 3 \]

  4. Divide by 3: \[ x = \frac{3}{3} \] So: \[ x = 1 \]

Final Solution: \[ x = 1 \]

Verification:

Substituting \(x = 1\) back into the original equation: \[ 4(1 - 4) = 1 - 13 \] Calculating both sides: Left side: \[ 4(-3) = -12 \] Right side: \[ 1 - 13 = -12 \] Both sides are equal, verifying that \(x = 1\) is correct.

Summary:

The solution to the equation \(4(x - 4) = x - 13\) is \(x = 1\).