If $\frac{6}{x+1}=\frac{3}{2}$, then $x$ equals

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-104.jpg?height=436&width=523&top_left_y=1327&top_left_x=1191)
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Solution 1

Rewriting $\frac{3}{2}$ as $\frac{6}{4}$, we see that $\frac{6}{x+1}=\frac{6}{4}$ and so comparing denominators, $x+1=4$ or $x=3$.

Solution 2

Since $\frac{6}{x+1}=\frac{3}{2}$, then cross-multiplying, we obtain $2(6)=3(x+1)$ or $12=3 x+3$ or $3 x=9$ or $x=3$.

Solution 3

Inverting both sides of the equation, we get $\frac{x+1}{6}=\frac{2}{3}$ or $x+1=6 \times \frac{2}{3}=4$.

Thus, $x=3$.

ANSWER: (C)