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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x+3 by each term of 2-\frac{1}{2}x.

$$2x+x\left(-\frac{1}{2}\right)x+6+3\left(-\frac{1}{2}\right)x$$

Multiply x and x to get x^{2}.

$$2x+x^{2}\left(-\frac{1}{2}\right)+6+3\left(-\frac{1}{2}\right)x$$

Express 3\left(-\frac{1}{2}\right) as a single fraction.

$$2x+x^{2}\left(-\frac{1}{2}\right)+6+\frac{3\left(-1\right)}{2}x$$

Multiply 3 and -1 to get -3.

$$2x+x^{2}\left(-\frac{1}{2}\right)+6+\frac{-3}{2}x$$

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

$$2x+x^{2}\left(-\frac{1}{2}\right)+6-\frac{3}{2}x$$

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

$$\frac{1}{2}x+x^{2}\left(-\frac{1}{2}\right)+6$$

Expand

$$-\frac{x^{2}}{2}+\frac{x}{2}+6$$

Solution Steps

Apply the distributive property by multiplying each term of x+3 by each term of 2-\frac{1}{2}x.

$$2x+x\left(-\frac{1}{2}\right)x+6+3\left(-\frac{1}{2}\right)x$$

Multiply x and x to get x^{2}.

$$2x+x^{2}\left(-\frac{1}{2}\right)+6+3\left(-\frac{1}{2}\right)x$$

Express 3\left(-\frac{1}{2}\right) as a single fraction.

$$2x+x^{2}\left(-\frac{1}{2}\right)+6+\frac{3\left(-1\right)}{2}x$$

Multiply 3 and -1 to get -3.

$$2x+x^{2}\left(-\frac{1}{2}\right)+6+\frac{-3}{2}x$$

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

$$2x+x^{2}\left(-\frac{1}{2}\right)+6-\frac{3}{2}x$$

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

$$\frac{1}{2}x+x^{2}\left(-\frac{1}{2}\right)+6$$