Question

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Part 1
Solve the equation. Check your solution.
8 plus 7 q equals 12 plus 6 q

Answer 1

To solve the equation \( 8 + 7q = 12 + 6q \), follow these steps:

### Step 1: Get all terms involving \( q \) on one side and constant terms on the other side.

Subtract \( 6q \) from both sides:
\[
8 + 7q - 6q = 12 + 6q - 6q
\]
This simplifies to:
\[
8 + q = 12
\]

### Step 2: Isolate \( q \).

Subtract 8 from both sides:
\[
q = 12 - 8
\]
So,
\[
q = 4
\]

### Step 3: Check the solution.

Substitute \( q = 4 \) back into the original equation:
\[
8 + 7(4) = 12 + 6(4)
\]
Calculating both sides:
\[
8 + 28 = 12 + 24
\]
This simplifies to:
\[
36 = 36
\]

Since both sides are equal, our solution is confirmed.

### Final answer:
\[
q = 4
\]