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.