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

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

Solve for x

$$x=-10$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$4\left(\frac{x}{2}-6\right)=24\left(\frac{x}{3}+\frac{3}{2}\right)$$

Use the distributive property to multiply 4 by \frac{x}{2}-6.

$$4\times \frac{x}{2}-24=24\left(\frac{x}{3}+\frac{3}{2}\right)$$

Cancel out 2, the greatest common factor in 4 and 2.

$$2x-24=24\left(\frac{x}{3}+\frac{3}{2}\right)$$

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

$$2x-24=24\left(\frac{2x}{6}+\frac{3\times 3}{6}\right)$$

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

$$2x-24=24\times \frac{2x+3\times 3}{6}$$

Do the multiplications in 2x+3\times 3.

$$2x-24=24\times \frac{2x+9}{6}$$

Cancel out 6, the greatest common factor in 24 and 6.

$$2x-24=4\left(2x+9\right)$$

Use the distributive property to multiply 4 by 2x+9.

$$2x-24=8x+36$$

Subtract 8x from both sides.

$$2x-24-8x=36$$

Combine 2x and -8x to get -6x.

$$-6x-24=36$$

Add 24 to both sides.

$$-6x=36+24$$

Add 36 and 24 to get 60.

$$-6x=60$$

Divide both sides by -6.

$$x=\frac{60}{-6}$$

Divide 60 by -6 to get -10.

$$x=-10$$