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

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

Evaluate

$$\frac{x+10}{6}$$

Solution Steps

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

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

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

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

Divide -4 by 2 to get -2.

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

Express -\frac{1}{2}\left(-3\right) as a single fraction.

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

Multiply -1 and -3 to get 3.

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

Subtract 2 from -3 to get -5.

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

Combine x and \frac{3}{2}x to get \frac{5}{2}x.

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

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

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

Multiply -\frac{1}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-5}{3\times 2}.

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

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

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

Express -\frac{1}{3}\left(-5\right) as a single fraction.

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

Multiply -1 and -5 to get 5.

$$x-\frac{5}{6}x+\frac{5}{3}$$

Combine x and -\frac{5}{6}x to get \frac{1}{6}x.

$$\frac{1}{6}x+\frac{5}{3}$$

Expand

$$\frac{x}{6}+\frac{5}{3}$$

Solution Steps

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

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

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

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

Divide -4 by 2 to get -2.

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

Express -\frac{1}{2}\left(-3\right) as a single fraction.

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

Multiply -1 and -3 to get 3.

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

Subtract 2 from -3 to get -5.

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

Combine x and \frac{3}{2}x to get \frac{5}{2}x.

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

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

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

Multiply -\frac{1}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-5}{3\times 2}.

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

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

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

Express -\frac{1}{3}\left(-5\right) as a single fraction.

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

Multiply -1 and -5 to get 5.

$$x-\frac{5}{6}x+\frac{5}{3}$$

Combine x and -\frac{5}{6}x to get \frac{1}{6}x.

$$\frac{1}{6}x+\frac{5}{3}$$