# Calculate: /(1) 4 (2-x)+/(3) 2 = 3 (x-2)

## Expression: $$\frac { 1 } { 4 } ( 2 - x ) + \frac { 3 } { 2 } = 3 ( x - 2 )$$

Use the distributive property to multiply $\frac{1}{4}$ by $2-x$.

$$\frac{1}{4}\times 2+\frac{1}{4}\left(-1\right)x+\frac{3}{2}=3\left(x-2\right)$$

Multiply $\frac{1}{4}$ and $2$ to get $\frac{2}{4}$.

$$\frac{2}{4}+\frac{1}{4}\left(-1\right)x+\frac{3}{2}=3\left(x-2\right)$$

Reduce the fraction $\frac{2}{4}$ to lowest terms by extracting and canceling out $2$.

$$\frac{1}{2}+\frac{1}{4}\left(-1\right)x+\frac{3}{2}=3\left(x-2\right)$$

Multiply $\frac{1}{4}$ and $-1$ to get $-\frac{1}{4}$.

$$\frac{1}{2}-\frac{1}{4}x+\frac{3}{2}=3\left(x-2\right)$$

Since $\frac{1}{2}$ and $\frac{3}{2}$ have the same denominator, add them by adding their numerators.

$$\frac{1+3}{2}-\frac{1}{4}x=3\left(x-2\right)$$

Add $1$ and $3$ to get $4$.

$$\frac{4}{2}-\frac{1}{4}x=3\left(x-2\right)$$

Divide $4$ by $2$ to get $2$.

$$2-\frac{1}{4}x=3\left(x-2\right)$$

Use the distributive property to multiply $3$ by $x-2$.

$$2-\frac{1}{4}x=3x-6$$

Subtract $3x$ from both sides.

$$2-\frac{1}{4}x-3x=-6$$

Combine $-\frac{1}{4}x$ and $-3x$ to get $-\frac{13}{4}x$.

$$2-\frac{13}{4}x=-6$$

Subtract $2$ from both sides.

$$-\frac{13}{4}x=-6-2$$

Subtract $2$ from $-6$ to get $-8$.

$$-\frac{13}{4}x=-8$$

Multiply both sides by $-\frac{4}{13}$, the reciprocal of $-\frac{13}{4}$.

$$x=-8\left(-\frac{4}{13}\right)$$

Express $-8\left(-\frac{4}{13}\right)$ as a single fraction.

$$x=\frac{-8\left(-4\right)}{13}$$

Multiply $-8$ and $-4$ to get $32$.

$$x=\frac{32}{13}$$

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