Questions: Solve the following equation. Make sure you verify your answers. Write fractions in the form of a / b. If your answer includes a square root estimate it to one decimal place. If there is no solution write none in the both answer boxes. If there is an extraneous root put ext in the second answer box. x-5=4

Solution Steps

The equation \( |x - 5| = 4 \) means that the expression inside the absolute value, \( x - 5 \), can be either \( 4 \) or \( -4 \).

Set \( x - 5 = 4 \) and solve for \( x \): \[ x - 5 = 4 \\ x = 4 + 5 \\ x = 9 \]

Set \( x - 5 = -4 \) and solve for \( x \): \[ x - 5 = -4 \\ x = -4 + 5 \\ x = 1 \]

Substitute \( x = 9 \) into the original equation: \[ |9 - 5| = |4| = 4 \quad \text{(Valid)} \]

Substitute \( x = 1 \) into the original equation: \[ |1 - 5| = |-4| = 4 \quad \text{(Valid)} \]

Both solutions are valid, so there are no extraneous roots.

Final Answer