Question

Solve the equation. Check your solution.
11 plus 9 q equals 12 plus 8 q

Answer 1

To solve the equation \( 11 + 9q = 12 + 8q \), we start by isolating the variable \( q \).

1. Subtract \( 8q \) from both sides to get all the \( q \) terms on one side:
\[
11 + 9q - 8q = 12 + 8q - 8q
\]
This simplifies to:
\[
11 + q = 12
\]

2. Next, subtract 11 from both sides to isolate \( q \):
\[
q = 12 - 11
\]
Therefore:
\[
q = 1
\]

Now, let's check the solution by substituting \( q = 1 \) back into the original equation:

The original equation is:
\[
11 + 9q = 12 + 8q
\]

Substituting \( q = 1 \):
\[
11 + 9(1) = 12 + 8(1)
\]
Which simplifies to:
\[
11 + 9 = 12 + 8
\]
And further simplifies to:
\[
20 = 20
\]

Since both sides of the equation are equal, the solution \( q = 1 \) is verified.

Thus, the solution to the equation \( 11 + 9q = 12 + 8q \) is:
\[
\boxed{1}
\]