Question
Solve Two-Step Linear Equations Quick Check
3 of 53 of 5 Items
Question
Solve for x
.
11/4x+9=31
(1 point)
Responses
x=−8
x equals negative 8
x=8
x equals 8
x=110
x equals 110
x=22
Answers
GPT-4o mini
To solve the equation \(\frac{11}{4}x + 9 = 31\), follow these steps:
1. Subtract 9 from both sides to isolate the term with \(x\):
\[
\frac{11}{4}x = 31 - 9
\]
\[
\frac{11}{4}x = 22
\]
2. Now, multiply both sides by the reciprocal of \(\frac{11}{4}\), which is \(\frac{4}{11}\):
\[
x = 22 \cdot \frac{4}{11}
\]
\[
x = \frac{88}{11} = 8
\]
Thus, the solution is:
\[
x = 8
\]
Therefore, the correct response is:
**x = 8**.
1. Subtract 9 from both sides to isolate the term with \(x\):
\[
\frac{11}{4}x = 31 - 9
\]
\[
\frac{11}{4}x = 22
\]
2. Now, multiply both sides by the reciprocal of \(\frac{11}{4}\), which is \(\frac{4}{11}\):
\[
x = 22 \cdot \frac{4}{11}
\]
\[
x = \frac{88}{11} = 8
\]
Thus, the solution is:
\[
x = 8
\]
Therefore, the correct response is:
**x = 8**.