Solve 1/2(x+3)+3/4(2/3x-10/3)

$$\frac { 1 } { 2 } ( x + 3 ) + \frac { 3 } { 4 } ( \frac { 2 } { 3 } x - \frac { 10 } { 3 } )$$

Evaluate

$$x-1$$

Solution Steps

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

$$\frac{1}{2}x+\frac{1}{2}\times 3+\frac{3}{4}\left(\frac{2}{3}x-\frac{10}{3}\right)$$

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

$$\frac{1}{2}x+\frac{3}{2}+\frac{3}{4}\left(\frac{2}{3}x-\frac{10}{3}\right)$$

Use the distributive property to multiply \frac{3}{4} by \frac{2}{3}x-\frac{10}{3}.

$$\frac{1}{2}x+\frac{3}{2}+\frac{3}{4}\times \frac{2}{3}x+\frac{3}{4}\left(-\frac{10}{3}\right)$$

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}x+\frac{3}{2}+\frac{3\times 2}{4\times 3}x+\frac{3}{4}\left(-\frac{10}{3}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{2}x+\frac{3}{2}+\frac{2}{4}x+\frac{3}{4}\left(-\frac{10}{3}\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x+\frac{3}{2}+\frac{1}{2}x+\frac{3}{4}\left(-\frac{10}{3}\right)$$

Multiply \frac{3}{4} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}x+\frac{3}{2}+\frac{1}{2}x+\frac{3\left(-10\right)}{4\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{2}x+\frac{3}{2}+\frac{1}{2}x+\frac{-10}{4}$$

Reduce the fraction \frac{-10}{4} to lowest terms by extracting and canceling out 2.

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

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

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

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

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

Subtract 5 from 3 to get -2.

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

Divide -2 by 2 to get -1.

$$x-1$$

Expand

$$x-1$$

Solution Steps

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

$$\frac{1}{2}x+\frac{1}{2}\times 3+\frac{3}{4}\left(\frac{2}{3}x-\frac{10}{3}\right)$$

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

$$\frac{1}{2}x+\frac{3}{2}+\frac{3}{4}\left(\frac{2}{3}x-\frac{10}{3}\right)$$

Use the distributive property to multiply \frac{3}{4} by \frac{2}{3}x-\frac{10}{3}.

$$\frac{1}{2}x+\frac{3}{2}+\frac{3}{4}\times \frac{2}{3}x+\frac{3}{4}\left(-\frac{10}{3}\right)$$

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}x+\frac{3}{2}+\frac{3\times 2}{4\times 3}x+\frac{3}{4}\left(-\frac{10}{3}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{2}x+\frac{3}{2}+\frac{2}{4}x+\frac{3}{4}\left(-\frac{10}{3}\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x+\frac{3}{2}+\frac{1}{2}x+\frac{3}{4}\left(-\frac{10}{3}\right)$$

Multiply \frac{3}{4} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}x+\frac{3}{2}+\frac{1}{2}x+\frac{3\left(-10\right)}{4\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{2}x+\frac{3}{2}+\frac{1}{2}x+\frac{-10}{4}$$

Reduce the fraction \frac{-10}{4} to lowest terms by extracting and canceling out 2.

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

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

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

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

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

Subtract 5 from 3 to get -2.

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

Divide -2 by 2 to get -1.

$$x-1$$