Solve 1/3(9x+5)-1/2(6x-2)

$$\frac { 1 } { 3 } ( 9 x + 5 ) - \frac { 1 } { 2 } ( 6 x - 2 )$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by 9x+5.

$$\frac{1}{3}\times 9x+\frac{1}{3}\times 5-\frac{1}{2}\left(6x-2\right)$$

Multiply \frac{1}{3} and 9 to get \frac{9}{3}.

$$\frac{9}{3}x+\frac{1}{3}\times 5-\frac{1}{2}\left(6x-2\right)$$

Divide 9 by 3 to get 3.

$$3x+\frac{1}{3}\times 5-\frac{1}{2}\left(6x-2\right)$$

Multiply \frac{1}{3} and 5 to get \frac{5}{3}.

$$3x+\frac{5}{3}-\frac{1}{2}\left(6x-2\right)$$

Use the distributive property to multiply -\frac{1}{2} by 6x-2.

$$3x+\frac{5}{3}-\frac{1}{2}\times 6x-\frac{1}{2}\left(-2\right)$$

Express -\frac{1}{2}\times 6 as a single fraction.

$$3x+\frac{5}{3}+\frac{-6}{2}x-\frac{1}{2}\left(-2\right)$$

Divide -6 by 2 to get -3.

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

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

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

Multiply -1 and -2 to get 2.

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

Divide 2 by 2 to get 1.

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

Combine 3x and -3x to get 0.

$$\frac{5}{3}+1$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{5}{3}+\frac{3}{3}$$

Since \frac{5}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$\frac{5+3}{3}$$

Add 5 and 3 to get 8.

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{9x+5-3\left(3x-1\right)}{3}$$

Simplify.

$$\frac{8}{3}$$