Absolutely! Let's double-check the solution for the equation \(\frac{11}{4}x + 9 = 31\).
-
Start with the original equation:
\[
\frac{11}{4}x + 9 = 31
\]
-
Subtract 9 from both sides:
\[
\frac{11}{4}x = 31 - 9
\]
This simplifies to:
\[
\frac{11}{4}x = 22
\]
-
Now, multiply both sides by the reciprocal of \(\frac{11}{4}\), which is \(\frac{4}{11}\):
\[
x = 22 \cdot \frac{4}{11}
\]
-
Calculate the right side:
\[
x = \frac{22 \times 4}{11} = \frac{88}{11} = 8
\]
Finally, we verify the solution by plugging \(x = 8\) back into the original equation:
\[
\frac{11}{4}(8) + 9 = 31
\]
Calculating the left side:
\[
\frac{11 \times 8}{4} + 9 = \frac{88}{4} + 9 = 22 + 9 = 31
\]
Since both sides equal 31, the solution \(x = 8\) is confirmed correct.
So the answer is indeed:
2. x = 8.