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

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

Evaluate

$$\frac{9y}{5}-\frac{28x}{15}-\frac{26}{15}$$

Solution Steps

Use the distributive property to multiply \frac{2}{5} by -3x+2y-1.

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

Express \frac{2}{5}\left(-3\right) as a single fraction.

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

Multiply 2 and -3 to get -6.

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

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

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

Express \frac{2}{5}\times 2 as a single fraction.

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

Multiply 2 and 2 to get 4.

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

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

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

Use the distributive property to multiply -\frac{1}{3} by 2x-3y+4.

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

Express -\frac{1}{3}\times 2 as a single fraction.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Express -\frac{1}{3}\left(-3\right) as a single fraction.

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

Multiply -1 and -3 to get 3.

$$-\frac{6}{5}x+\frac{4}{5}y-\frac{2}{5}-\frac{2}{3}x+\frac{3}{3}y-\frac{1}{3}\times 4$$

Divide 3 by 3 to get 1.

$$-\frac{6}{5}x+\frac{4}{5}y-\frac{2}{5}-\frac{2}{3}x+1y-\frac{1}{3}\times 4$$

Express -\frac{1}{3}\times 4 as a single fraction.

$$-\frac{6}{5}x+\frac{4}{5}y-\frac{2}{5}-\frac{2}{3}x+1y+\frac{-4}{3}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$-\frac{6}{5}x+\frac{4}{5}y-\frac{2}{5}-\frac{2}{3}x+1y-\frac{4}{3}$$

Combine -\frac{6}{5}x and -\frac{2}{3}x to get -\frac{28}{15}x.

$$-\frac{28}{15}x+\frac{4}{5}y-\frac{2}{5}+1y-\frac{4}{3}$$

Combine \frac{4}{5}y and 1y to get \frac{9}{5}y.

$$-\frac{28}{15}x+\frac{9}{5}y-\frac{2}{5}-\frac{4}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{2}{5} and \frac{4}{3} to fractions with denominator 15.

$$-\frac{28}{15}x+\frac{9}{5}y-\frac{6}{15}-\frac{20}{15}$$

Since -\frac{6}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{28}{15}x+\frac{9}{5}y+\frac{-6-20}{15}$$

Subtract 20 from -6 to get -26.

$$-\frac{28}{15}x+\frac{9}{5}y-\frac{26}{15}$$

Expand

$$\frac{9y}{5}-\frac{28x}{15}-\frac{26}{15}$$

Solution Steps

Use the distributive property to multiply \frac{2}{5} by -3x+2y-1.

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

Express \frac{2}{5}\left(-3\right) as a single fraction.

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

Multiply 2 and -3 to get -6.

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

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

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

Express \frac{2}{5}\times 2 as a single fraction.

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

Multiply 2 and 2 to get 4.

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

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

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

Use the distributive property to multiply -\frac{1}{3} by 2x-3y+4.

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

Express -\frac{1}{3}\times 2 as a single fraction.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Express -\frac{1}{3}\left(-3\right) as a single fraction.

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

Multiply -1 and -3 to get 3.

$$-\frac{6}{5}x+\frac{4}{5}y-\frac{2}{5}-\frac{2}{3}x+\frac{3}{3}y-\frac{1}{3}\times 4$$

Divide 3 by 3 to get 1.

$$-\frac{6}{5}x+\frac{4}{5}y-\frac{2}{5}-\frac{2}{3}x+1y-\frac{1}{3}\times 4$$

Express -\frac{1}{3}\times 4 as a single fraction.

$$-\frac{6}{5}x+\frac{4}{5}y-\frac{2}{5}-\frac{2}{3}x+1y+\frac{-4}{3}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$-\frac{6}{5}x+\frac{4}{5}y-\frac{2}{5}-\frac{2}{3}x+1y-\frac{4}{3}$$

Combine -\frac{6}{5}x and -\frac{2}{3}x to get -\frac{28}{15}x.

$$-\frac{28}{15}x+\frac{4}{5}y-\frac{2}{5}+1y-\frac{4}{3}$$

Combine \frac{4}{5}y and 1y to get \frac{9}{5}y.

$$-\frac{28}{15}x+\frac{9}{5}y-\frac{2}{5}-\frac{4}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{2}{5} and \frac{4}{3} to fractions with denominator 15.

$$-\frac{28}{15}x+\frac{9}{5}y-\frac{6}{15}-\frac{20}{15}$$

Since -\frac{6}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{28}{15}x+\frac{9}{5}y+\frac{-6-20}{15}$$

Subtract 20 from -6 to get -26.

$$-\frac{28}{15}x+\frac{9}{5}y-\frac{26}{15}$$