Question

chris wrote an equation and the first step of his solution process, as shown.
$16 = 12 - 6x$
$4 = -6x$
which math operation did chris apply in his first step?
a he divided 16 by 4.
b he added 12 to each side of the equation.
c he divided each side of the equation by 4.
d he subtracted 12 from each side of the equation.

Explanation:

Step1: Analyze the original equation and the first step

The original equation is \(16 = 12 - 6x\), and the first step result is \(4=-6x\). Let's check each option:

• Option A: Dividing 16 by 4 is not related to transforming the equation from \(16 = 12 - 6x\) to \(4=-6x\), so A is wrong.
• Option B: If we add 12 to each side, the left side would be \(16 + 12=28\), and the right side would be \(12 - 6x+ 12 = 24-6x\), which is not \(4=-6x\), so B is wrong.
• Option C: Dividing each side by 4, the left side would be \(\frac{16}{4} = 4\), and the right side would be \(\frac{12 - 6x}{4}=\frac{12}{4}-\frac{6x}{4}=3-\frac{3x}{2}\), which is not \(-6x\), so C is wrong.
• Option D: Subtract 12 from each side. For the left side: \(16-12 = 4\). For the right side: \(12 - 6x-12=-6x\). So we get \(4=-6x\), which matches the first step. So D is correct.

Answer:

D. He subtracted 12 from each side of the equation.