Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( k = -9 \)
Solution
To solve the equation for \( k \):
\[
-6k - 2 = 106 + 6k
\]
**Step 1: Gather like terms.**
First, let's move all terms containing \( k \) to one side and the constant terms to the other side. To do this, add \( 6k \) to both sides of the equation:
\[
-6k - 2 + 6k = 106 + 6k + 6k
\]
Simplifying both sides:
\[
-2 = 106 + 12k
\]
**Step 2: Isolate the term with \( k \).**
Next, subtract \( 106 \) from both sides to isolate the term with \( k \):
\[
-2 - 106 = 12k
\]
Simplifying:
\[
-108 = 12k
\]
**Step 3: Solve for \( k \).**
Finally, divide both sides by \( 12 \) to solve for \( k \):
\[
k = \frac{-108}{12} = -9
\]
**Solution:**
\[
k = -9
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To solve for \( k \) in the equation \( -6k - 2 = 106 + 6k \), first, let's move all terms involving \( k \) to one side and constant terms to the other side. Add \( 6k \) to both sides: \[ -6k - 6k - 2 = 106 \] This simplifies to: \[ -12k - 2 = 106 \] Next, add \( 2 \) to both sides: \[ -12k = 106 + 2 \] This gives: \[ -12k = 108 \] Now, divide both sides by \( -12 \): \[ k = \frac{108}{-12} \] Thus: \[ k = -9 \] So, the solution is \( k = -9 \).
