Solve 3x-6(x/2+1/3)-4(x-1)

$$3 x - 6 ( \frac { x } { 2 } + \frac { 1 } { 3 } ) - 4 ( x - 1 )$$

Evaluate

$$2-4x$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{x}{2} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{2}{2}.

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

Since \frac{3x}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

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

Cancel out 6 and 6.

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

To find the opposite of 3x+2, find the opposite of each term.

$$3x-3x-2-4\left(x-1\right)$$

Combine 3x and -3x to get 0.

$$-2-4\left(x-1\right)$$

Use the distributive property to multiply -4 by x-1.

$$-2-4x+4$$

Add -2 and 4 to get 2.

$$2-4x$$

Expand

$$2-4x$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{x}{2} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{2}{2}.

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

Since \frac{3x}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

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

Cancel out 6 and 6.

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

To find the opposite of 3x+2, find the opposite of each term.

$$3x-3x-2-4\left(x-1\right)$$

Combine 3x and -3x to get 0.

$$-2-4\left(x-1\right)$$

Use the distributive property to multiply -4 by x-1.

$$-2-4x+4$$

Add -2 and 4 to get 2.

$$2-4x$$