Solve (x-1/3)(x/2+4)=

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

Evaluate

$$\frac{\left(3x-1\right)\left(x+8\right)}{6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

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

Since \frac{x}{2} and \frac{4\times 2}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x+4\times 2.

$$\left(x-\frac{1}{3}\right)\times \frac{x+8}{2}$$

Use the distributive property to multiply x-\frac{1}{3} by \frac{x+8}{2}.

$$x\times \frac{x+8}{2}-\frac{1}{3}\times \frac{x+8}{2}$$

Express x\times \frac{x+8}{2} as a single fraction.

$$\frac{x\left(x+8\right)}{2}-\frac{1}{3}\times \frac{x+8}{2}$$

Multiply -\frac{1}{3} times \frac{x+8}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\left(x+8\right)}{2}+\frac{-\left(x+8\right)}{3\times 2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3\times 2 is 2\times 3. Multiply \frac{x\left(x+8\right)}{2} times \frac{3}{3}.

$$\frac{3x\left(x+8\right)}{2\times 3}+\frac{-\left(x+8\right)}{2\times 3}$$

Since \frac{3x\left(x+8\right)}{2\times 3} and \frac{-\left(x+8\right)}{2\times 3} have the same denominator, add them by adding their numerators.

$$\frac{3x\left(x+8\right)-\left(x+8\right)}{2\times 3}$$

Do the multiplications in 3x\left(x+8\right)-\left(x+8\right).

$$\frac{3x^{2}+24x-x-8}{2\times 3}$$

Combine like terms in 3x^{2}+24x-x-8.

$$\frac{3x^{2}+23x-8}{2\times 3}$$

Expand 2\times 3.

$$\frac{3x^{2}+23x-8}{6}$$

Expand

$$\frac{x^{2}}{2}+\frac{23x}{6}-\frac{4}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

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

Since \frac{x}{2} and \frac{4\times 2}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x+4\times 2.

$$\left(x-\frac{1}{3}\right)\times \frac{x+8}{2}$$

Use the distributive property to multiply x-\frac{1}{3} by \frac{x+8}{2}.

$$x\times \frac{x+8}{2}-\frac{1}{3}\times \frac{x+8}{2}$$

Express x\times \frac{x+8}{2} as a single fraction.

$$\frac{x\left(x+8\right)}{2}-\frac{1}{3}\times \frac{x+8}{2}$$

Multiply -\frac{1}{3} times \frac{x+8}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x\left(x+8\right)}{2}+\frac{-\left(x+8\right)}{3\times 2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3\times 2 is 2\times 3. Multiply \frac{x\left(x+8\right)}{2} times \frac{3}{3}.

$$\frac{3x\left(x+8\right)}{2\times 3}+\frac{-\left(x+8\right)}{2\times 3}$$

Since \frac{3x\left(x+8\right)}{2\times 3} and \frac{-\left(x+8\right)}{2\times 3} have the same denominator, add them by adding their numerators.

$$\frac{3x\left(x+8\right)-\left(x+8\right)}{2\times 3}$$

Do the multiplications in 3x\left(x+8\right)-\left(x+8\right).

$$\frac{3x^{2}+24x-x-8}{2\times 3}$$

Combine like terms in 3x^{2}+24x-x-8.

$$\frac{3x^{2}+23x-8}{2\times 3}$$

Expand 2\times 3.

$$\frac{3x^{2}+23x-8}{6}$$