Question

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Part 1
Solve the equation. Check your solution.
3 plus 7 q equals 5 plus 6 q

Answer 1

To solve the equation \(3 + 7q = 5 + 6q\), we can follow these steps:

1. **Isolate the variable**: Start by moving the terms involving \(q\) to one side of the equation and the constant terms to the other side.

Subtract \(6q\) from both sides:
\[
3 + 7q - 6q = 5
\]

Simplifying this gives:
\[
3 + q = 5
\]

2. **Isolate \(q\)**: Next, subtract \(3\) from both sides:
\[
q = 5 - 3
\]
Thus,
\[
q = 2
\]

Now we have \(q = 2\).

### Check the solution
To verify our solution, we can substitute \(q = 2\) back into the original equation and see if both sides are equal.

Substituting in:
\[
3 + 7(2) = 5 + 6(2)
\]

Calculating the left side:
\[
3 + 14 = 17
\]

Calculating the right side:
\[
5 + 12 = 17
\]

Since both sides are equal (\(17 = 17\)), our solution is verified.

### Final answer
The solution to the equation is:
\[
q = 2
\]