Solve Two-Step Linear Equations Quick Check

Question

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

Answer 1

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.