Solve the following: 1 4 (x-2)+2 3 (2x-1)=5 6 x+2

MCQ

Solve the following: $\frac{1}{4}(\text{x}-2)+\frac{2}{3}(\text{2x}-1)=\frac{5}{6}\text{x}+2$

A
$\frac{3}{2}$
B
$-\frac{2}{3}$
✓
$\frac{2}{3}$
D
$-\frac{3}{2}$

✓

Answer

Correct option: C.

$\frac{2}{3}$

$\frac{1}{4}(\text{x}-2)+\frac{2}{3}(\text{2x}-1)=\frac{5}{6}\text{x}+2$
$\Rightarrow\frac{\text{x}}{4}+\frac{\text{2}}{4}+\frac{\text{4x}}{4}+\frac{\text{2}}{3}=\frac{\text{5x}}{6}+\frac{\text{10}}{6}$
$\Rightarrow\frac{\text{x}}{4}+\frac{\text{4x}}{3}-\frac{\text{5x}}{6}=\frac{\text{10}}{6}-\frac{\text{2}}{4}-\frac{\text{2}}{4}$
$\Rightarrow\frac{\text{4x+16x-10x}}{12}=\frac{\text{20-6-8}}{12}$
$\Rightarrow\frac{\text{9x}}{12}=\frac{\text{6}}{12}$
$\Rightarrow\text{9x}=6$
$\Rightarrow\text{x}=\frac{\text{6}}{9}$
$\Rightarrow\text{x}=\frac{\text{2}}{3}$

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