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

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

Evaluate

$$-\frac{2x}{3}+y-\frac{11}{6}$$

Solution Steps

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

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

Express -\frac{1}{2}\times 4 as a single fraction.

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

Divide -4 by 2 to get -2.

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

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

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

Multiply -1 and -2 to get 2.

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

Divide 2 by 2 to get 1.

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

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

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

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

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

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

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

Express -\frac{1}{3}\left(-4\right) as a single fraction.

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

Multiply -1 and -4 to get 4.

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

Combine -2x and \frac{4}{3}x to get -\frac{2}{3}x.

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

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{1}{3} to fractions with denominator 6.

$$-\frac{2}{3}x+1y-\frac{9}{6}-\frac{2}{6}$$

Since -\frac{9}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}x+1y+\frac{-9-2}{6}$$

Subtract 2 from -9 to get -11.

$$-\frac{2}{3}x+1y-\frac{11}{6}$$

For any term t, t\times 1=t and 1t=t.

$$-\frac{2}{3}x+y-\frac{11}{6}$$

Expand

$$-\frac{2x}{3}+y-\frac{11}{6}$$

Solution Steps

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

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

Express -\frac{1}{2}\times 4 as a single fraction.

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

Divide -4 by 2 to get -2.

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

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

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

Multiply -1 and -2 to get 2.

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

Divide 2 by 2 to get 1.

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

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

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

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

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

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

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

Express -\frac{1}{3}\left(-4\right) as a single fraction.

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

Multiply -1 and -4 to get 4.

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

Combine -2x and \frac{4}{3}x to get -\frac{2}{3}x.

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

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{1}{3} to fractions with denominator 6.

$$-\frac{2}{3}x+1y-\frac{9}{6}-\frac{2}{6}$$

Since -\frac{9}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}x+1y+\frac{-9-2}{6}$$

Subtract 2 from -9 to get -11.

$$-\frac{2}{3}x+1y-\frac{11}{6}$$

For any term t, t\times 1=t and 1t=t.

$$-\frac{2}{3}x+y-\frac{11}{6}$$