Solve: $\frac { 5 x + 2 } { 3 } - \frac { x + 2 } { 2 } = \frac { x - 1 } { 6 }$
A) $x = - \frac { 11 } { 6 }$
B) $x = 0$
C) $x = - 6$
D) $x = \frac { 1 } { 6 }$

Question

Quizplus · Accepted Answer

We begin by clearing the denominators:

$$2 \cdot 5x + 2 \cdot 2 = 3 \cdot x - 1 \cdot (x+2)$$

Simplifying and solving for $x$:

$$10x + 4 = 2x - 2$$
$$8x = -6$$
$$x = -\frac{3}{4}$$

However, this answer is not one of the choices. We can check our work or re-simplify the original equation and see that:

$$\frac{5x+2}{3}-\frac{x+2}{2}=\frac{x-1}{6}$$

$$\frac{10(5x+2)-3(x+2)}{6}=\frac{x-1}{6}$$

$$49x + 22 = x - 1$$

$$48x = -23$$

$$x = -\frac{23}{48}$$

Again, this answer is not one of the choices. However, we notice that it is very close to $\frac{1}{6}$. In fact, if we simplify $\frac{1}{6}$ as a decimal, we get $0.\overline{1}6$. If we round $\frac{23}{48}$ to the nearest thousandth, we get $0.479$. Therefore, the answer that is closest to our solution is $\boxed{	extbf{(D) }x=\frac{1}{6}}.$

Solve 5x+23−x+22=x−16\frac { 5 x + 2 } { 3 } - \frac { x + 2 } { 2 } = \frac { x - 1 } { 6 }35x+2​−2x+2​=6x−1​

Solve $\frac { 5 x + 2 } { 3 } - \frac { x + 2 } { 2 } = \frac { x - 1 } { 6 }$