Question

1. max is solving the equation below.

3x - 2 = 10
which of the following are correct steps to find the solution?
a divide both sides by 3, then add 2 to both sides.
b add 2 to both sides, then divide both sides by 3.
c subtract 2 from both sides, then divide both sides by 3.

Explanation:

Step1: Analyze the equation \(3x - 2 = 10\)

We need to isolate \(x\). The term with \(x\) is \(3x\), and there is a \(-2\) attached to it. To get rid of the \(-2\) first, we use the inverse operation. The inverse of subtraction is addition, so we add 2 to both sides.

Step2: Add 2 to both sides

Adding 2 to both sides of the equation \(3x - 2 = 10\) gives:
\(3x - 2 + 2 = 10 + 2\)
Simplifying, we get \(3x = 12\).

Step3: Divide both sides by 3

Now, to isolate \(x\), we divide both sides of the equation \(3x = 12\) by 3:
\(\frac{3x}{3}=\frac{12}{3}\)
Simplifying, we get \(x = 4\).

Now let's check the options:

• Option A: Dividing by 3 first would give \(\frac{3x - 2}{3}=\frac{10}{3}\), which complicates isolating \(x\) as we still have a \(-\frac{2}{3}\) term. So A is incorrect.
• Option B: As we did above, adding 2 first and then dividing by 3 works. So B is correct.
• Option C: Subtracting 2 would give \(3x - 2 - 2 = 10 - 2\) or \(3x - 4 = 8\), which moves us further from isolating \(x\). So C is incorrect.

Answer:

B. Add 2 to both sides, then divide both sides by 3.