Solve 1/2(2x-3)-1/3(2-x)

$$\frac { 1 } { 2 } ( 2 x - 3 ) - \frac { 1 } { 3 } ( 2 - x )$$

Evaluate

$$\frac{4x}{3}-\frac{13}{6}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2x-3.

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

Cancel out 2 and 2.

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

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

Use the distributive property to multiply -\frac{1}{3} by 2-x.

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

Express -\frac{1}{3}\times 2 as a single fraction.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Multiply -\frac{1}{3} and -1 to get \frac{1}{3}.

$$x-\frac{3}{2}-\frac{2}{3}+\frac{1}{3}x$$

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{2}{3} to fractions with denominator 6.

$$x-\frac{9}{6}-\frac{4}{6}+\frac{1}{3}x$$

Since -\frac{9}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$x+\frac{-9-4}{6}+\frac{1}{3}x$$

Subtract 4 from -9 to get -13.

$$x-\frac{13}{6}+\frac{1}{3}x$$

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

$$\frac{4}{3}x-\frac{13}{6}$$

Expand

$$\frac{4x}{3}-\frac{13}{6}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2x-3.

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

Cancel out 2 and 2.

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

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

Use the distributive property to multiply -\frac{1}{3} by 2-x.

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

Express -\frac{1}{3}\times 2 as a single fraction.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Multiply -\frac{1}{3} and -1 to get \frac{1}{3}.

$$x-\frac{3}{2}-\frac{2}{3}+\frac{1}{3}x$$

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{2}{3} to fractions with denominator 6.

$$x-\frac{9}{6}-\frac{4}{6}+\frac{1}{3}x$$

Since -\frac{9}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$x+\frac{-9-4}{6}+\frac{1}{3}x$$

Subtract 4 from -9 to get -13.

$$x-\frac{13}{6}+\frac{1}{3}x$$

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

$$\frac{4}{3}x-\frac{13}{6}$$