Question

1. mr. greer solved the equation as shown below. however, when he checked his solution, it did not make the original equation true. find his error and then find the correct solution.

$4x = 8(2x - 3)$
$4x = 16x - 3$
$-12x = -3$
$x = \frac{-3}{-12}$
$x = \frac{1}{4}$

Explanation:

Step1: Identify the error in distribution

Mr. Greer incorrectly expanded $8(2x - 3)$ as $16x - 3$; the correct expansion is $8\times2x - 8\times3 = 16x - 24$.

Step2: Write correct original equation

$4x = 16x - 24$

Step3: Isolate x terms on one side

Subtract $16x$ from both sides:
$4x - 16x = 16x - 24 - 16x$
$-12x = -24$

Step4: Solve for x

Divide both sides by $-12$:
$x = \frac{-24}{-12}$

Answer:

Error: Mr. Greer made a mistake in distributing the 8; he calculated $8(2x-3)$ as $16x-3$ instead of the correct $16x-24$.
Correct solution: $x=2$