Question

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

Explanation:

Step1: Analyze Step 1

To solve \(3k - 6=15\), we need to isolate \(3k\). The correct operation is to add 6 to both sides (using the addition property of equality), not subtract 6. Brian subtracted 6 from both sides, which is incorrect. Let's check the other steps for completeness.

Step2: Analyze Step 2

If we follow Brian's incorrect Step 1 (\(3k-6 - 6=15 - 6\)), we get \(3k-12 = 9\), not \(3k = 9\). But the main error starts at Step 1 because the operation to isolate \(3k\) is wrong. However, let's check the reasoning of each option:

• Option 1: Says Step 1 is wrong because he should not have subtracted 6 to isolate \(3k\). This is correct because to isolate \(3k\) in \(3k - 6=15\), we add 6 to both sides (since \(- 6+6 = 0\) to cancel the \(-6\) on the left).
• Option 2: Step 2 is wrong in calculation only if Step 1 was correct, but Step 1 is already wrong.
• Option 3: Dividing by 3 to isolate \(k\) from \(3k\) is correct (since \(\frac{3k}{3}=k\)).
• Option 4: \(\frac{3k}{3}=k\) is a correct simplification.

Answer:

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