Question

jocelyn attempts to solve the equation $x^2 - 4x = x(x - 6) + 24$, as shown.

given	$x^2 - 4x = x(x - 6) + 24$
step 1	$x^2 - 4x = x^2 - 6x + 24$
step 2	$x^2 + 2x - 24 = 0$
step 3	$(x - 4)(x + 6) = 0$
step 4	$x - 4 = 0$ $x + 6 = 0$
step 5	$x = 4, -6$

jocelyn made an error when solving the equation.
a. in which step is the error first seen?
b. what is a solution to the original equation?
a. step
b. $x = $

Explanation:

Step1: Analyze Step 2

Original equation after Step 1: \(x^2 - 4x = x^2 - 6x + 24\). To simplify, subtract \(x^2\) and add \(6x\) to both sides: \(x^2 - 4x - x^2 + 6x = 24\), which simplifies to \(2x = 24\), not \(x^2 + 2x - 24 = 0\). So error is in Step 2.

Step2: Solve original equation

Start with \(x^2 - 4x = x(x - 6) + 24\). Expand right side: \(x^2 - 4x = x^2 - 6x + 24\). Subtract \(x^2\) from both sides: \(-4x = -6x + 24\). Add \(6x\) to both sides: \(2x = 24\). Divide by 2: \(x = 12\).

Answer:

A. Step 2
B. \(x = 12\)