Question

brian tried to solve the equation 3k - 6 = 15. he wants to find and correct his error.
brian’s work is shown. where did he make
a mistake? choose the first incorrect step
in brian’s work.
step 1, because he should not have
subtracted 6 to isolate 3k
step 2, because 15 - 6 ≠ 9
step 3, because he should not have
divided by 3 to isolate k
step 4, because \\(\frac{3k}{3}\\) ≠ k
brian’s work
step 1 \\(\

$$\begin{align}3k - 6 &= 15\\\\ - 6 & - 6\\end{align}$$

\\)
step 2 \\(3k = 9\\)
step 3 \\(\frac{3k}{3} = \frac{9}{3}\\)
step 4 \\(k = 3\\)

Explanation:

To solve the equation \(3k - 6 = 15\), we need to isolate \(k\). The correct first step is to add 6 to both sides (to undo the subtraction of 6), not subtract 6. Let's analyze Brian's steps:

• Step 1: Brian subtracted 6 from both sides. The original equation is \(3k - 6 = 15\). To isolate \(3k\), we should add 6 to both sides (because we have \(-6\) on the left, so we use the inverse operation, addition). Subtracting 6 is incorrect here.
• Let's check the other options to be sure:
• Step 2: If Step 1 was wrong, Step 2 is a result of Step 1, but the first mistake is in Step 1. Also, \(15 - 6 = 9\) is correct mathematically, but the error is in the operation chosen in Step 1.
• Step 3: Dividing by 3 to isolate \(k\) is the correct inverse operation for \(3k\), so this step is not an error.
• Step 4: \(\frac{3k}{3}=k\) is correct, so this step is not an error.

So the first incorrect step is Step 1, because he should have added 6 (not subtracted 6) to isolate \(3k\).

Answer:

Step 1, because he should not have subtracted 6 to isolate \(3k\)