Solve 1/2(x-5)-1/2(x+3)

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

Evaluate

$$-4$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by x-5.

$$\frac{1}{2}x+\frac{1}{2}\left(-5\right)-\frac{1}{2}\left(x+3\right)$$

Multiply \frac{1}{2} and -5 to get \frac{-5}{2}.

$$\frac{1}{2}x+\frac{-5}{2}-\frac{1}{2}\left(x+3\right)$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$\frac{1}{2}x-\frac{5}{2}-\frac{1}{2}\left(x+3\right)$$

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

$$\frac{1}{2}x-\frac{5}{2}-\frac{1}{2}x-\frac{1}{2}\times 3$$

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

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

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

$$\frac{1}{2}x-\frac{5}{2}-\frac{1}{2}x-\frac{3}{2}$$

Combine \frac{1}{2}x and -\frac{1}{2}x to get 0.

$$-\frac{5}{2}-\frac{3}{2}$$

Since -\frac{5}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-3}{2}$$

Subtract 3 from -5 to get -8.

$$\frac{-8}{2}$$

Divide -8 by 2 to get -4.

$$-4$$

Factor

$$-4$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{x-5-\left(x+3\right)}{2}$$

Simplify.

$$-4$$