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

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

Evaluate

$$\frac{2x-11}{3}$$

Solution Steps

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

$$\frac{2}{3}x+\frac{2}{3}\times \frac{1}{2}-4$$

Multiply \frac{2}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}x+\frac{2\times 1}{3\times 2}-4$$

Cancel out 2 in both numerator and denominator.

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

Convert 4 to fraction \frac{12}{3}.

$$\frac{2}{3}x+\frac{1}{3}-\frac{12}{3}$$

Since \frac{1}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}x+\frac{1-12}{3}$$

Subtract 12 from 1 to get -11.

$$\frac{2}{3}x-\frac{11}{3}$$

Expand

$$\frac{2x-11}{3}$$

Solution Steps

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

$$\frac{2}{3}x+\frac{2}{3}\times \frac{1}{2}-4$$

Multiply \frac{2}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}x+\frac{2\times 1}{3\times 2}-4$$

Cancel out 2 in both numerator and denominator.

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

Convert 4 to fraction \frac{12}{3}.

$$\frac{2}{3}x+\frac{1}{3}-\frac{12}{3}$$

Since \frac{1}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}x+\frac{1-12}{3}$$

Subtract 12 from 1 to get -11.

$$\frac{2}{3}x-\frac{11}{3}$$