Question

solve for \(x\)
\(\frac{11}{4}x+9=31\)

Answer 1

To solve the equation \(\frac{11}{4}x + 9 = 31\), follow these steps:

1. Subtract 9 from both sides:
\[
\frac{11}{4}x + 9 - 9 = 31 - 9
\]
Simplifying this gives:
\[
\frac{11}{4}x = 22
\]

2. Next, to isolate \(x\), multiply both sides by the reciprocal of \(\frac{11}{4}\), which is \(\frac{4}{11}\):
\[
x = 22 \cdot \frac{4}{11}
\]
Now, simplify the right side:
\[
x = \frac{88}{11} = 8
\]

Thus, the solution is:
\[
\boxed{8}
\]