Solve 1/2(2x-5y+6)+1/3(4y-7)=

$$\frac { 1 } { 2 } ( 2 x - 5 y + 6 ) + \frac { 1 } { 3 } ( 4 y - 7 ) =$$

Evaluate

$$-\frac{7y}{6}+x+\frac{2}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2x-5y+6.

$$\frac{1}{2}\times 2x+\frac{1}{2}\left(-5\right)y+\frac{1}{2}\times 6+\frac{1}{3}\left(4y-7\right)$$

Cancel out 2 and 2.

$$x+\frac{1}{2}\left(-5\right)y+\frac{1}{2}\times 6+\frac{1}{3}\left(4y-7\right)$$

Multiply \frac{1}{2} and -5 to get \frac{-5}{2}.

$$x+\frac{-5}{2}y+\frac{1}{2}\times 6+\frac{1}{3}\left(4y-7\right)$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$x-\frac{5}{2}y+\frac{1}{2}\times 6+\frac{1}{3}\left(4y-7\right)$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$x-\frac{5}{2}y+\frac{6}{2}+\frac{1}{3}\left(4y-7\right)$$

Divide 6 by 2 to get 3.

$$x-\frac{5}{2}y+3+\frac{1}{3}\left(4y-7\right)$$

Use the distributive property to multiply \frac{1}{3} by 4y-7.

$$x-\frac{5}{2}y+3+\frac{1}{3}\times 4y+\frac{1}{3}\left(-7\right)$$

Multiply \frac{1}{3} and 4 to get \frac{4}{3}.

$$x-\frac{5}{2}y+3+\frac{4}{3}y+\frac{1}{3}\left(-7\right)$$

Multiply \frac{1}{3} and -7 to get \frac{-7}{3}.

$$x-\frac{5}{2}y+3+\frac{4}{3}y+\frac{-7}{3}$$

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$x-\frac{5}{2}y+3+\frac{4}{3}y-\frac{7}{3}$$

Combine -\frac{5}{2}y and \frac{4}{3}y to get -\frac{7}{6}y.

$$x-\frac{7}{6}y+3-\frac{7}{3}$$

Convert 3 to fraction \frac{9}{3}.

$$x-\frac{7}{6}y+\frac{9}{3}-\frac{7}{3}$$

Since \frac{9}{3} and \frac{7}{3} have the same denominator, subtract them by subtracting their numerators.

$$x-\frac{7}{6}y+\frac{9-7}{3}$$

Subtract 7 from 9 to get 2.

$$x-\frac{7}{6}y+\frac{2}{3}$$

Expand

$$-\frac{7y}{6}+x+\frac{2}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2x-5y+6.

$$\frac{1}{2}\times 2x+\frac{1}{2}\left(-5\right)y+\frac{1}{2}\times 6+\frac{1}{3}\left(4y-7\right)$$

Cancel out 2 and 2.

$$x+\frac{1}{2}\left(-5\right)y+\frac{1}{2}\times 6+\frac{1}{3}\left(4y-7\right)$$

Multiply \frac{1}{2} and -5 to get \frac{-5}{2}.

$$x+\frac{-5}{2}y+\frac{1}{2}\times 6+\frac{1}{3}\left(4y-7\right)$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$x-\frac{5}{2}y+\frac{1}{2}\times 6+\frac{1}{3}\left(4y-7\right)$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$x-\frac{5}{2}y+\frac{6}{2}+\frac{1}{3}\left(4y-7\right)$$

Divide 6 by 2 to get 3.

$$x-\frac{5}{2}y+3+\frac{1}{3}\left(4y-7\right)$$

Use the distributive property to multiply \frac{1}{3} by 4y-7.

$$x-\frac{5}{2}y+3+\frac{1}{3}\times 4y+\frac{1}{3}\left(-7\right)$$

Multiply \frac{1}{3} and 4 to get \frac{4}{3}.

$$x-\frac{5}{2}y+3+\frac{4}{3}y+\frac{1}{3}\left(-7\right)$$

Multiply \frac{1}{3} and -7 to get \frac{-7}{3}.

$$x-\frac{5}{2}y+3+\frac{4}{3}y+\frac{-7}{3}$$

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$x-\frac{5}{2}y+3+\frac{4}{3}y-\frac{7}{3}$$

Combine -\frac{5}{2}y and \frac{4}{3}y to get -\frac{7}{6}y.

$$x-\frac{7}{6}y+3-\frac{7}{3}$$

Convert 3 to fraction \frac{9}{3}.

$$x-\frac{7}{6}y+\frac{9}{3}-\frac{7}{3}$$

Since \frac{9}{3} and \frac{7}{3} have the same denominator, subtract them by subtracting their numerators.

$$x-\frac{7}{6}y+\frac{9-7}{3}$$

Subtract 7 from 9 to get 2.

$$x-\frac{7}{6}y+\frac{2}{3}$$