Solve 3/2[-2/3(x/4-1)-2]-x=2

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

Solve for x

$$x = -\frac{16}{5} = -3\frac{1}{5} = -3.2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,4.

$$18\left(-\frac{2}{3}\left(\frac{x}{4}-1\right)-2\right)-12x=24$$

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

$$18\left(-\frac{2}{3}\times \frac{x}{4}-\frac{2}{3}\left(-1\right)-2\right)-12x=24$$

Multiply -\frac{2}{3} times \frac{x}{4} by multiplying numerator times numerator and denominator times denominator.

$$18\left(\frac{-2x}{3\times 4}-\frac{2}{3}\left(-1\right)-2\right)-12x=24$$

Cancel out 2 in both numerator and denominator.

$$18\left(\frac{-x}{2\times 3}-\frac{2}{3}\left(-1\right)-2\right)-12x=24$$

Multiply -\frac{2}{3} and -1 to get \frac{2}{3}.

$$18\left(\frac{-x}{2\times 3}+\frac{2}{3}-2\right)-12x=24$$

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

$$18\left(\frac{-x}{2\times 3}+\frac{2\times 2}{2\times 3}-2\right)-12x=24$$

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

$$18\left(\frac{-x+2\times 2}{2\times 3}-2\right)-12x=24$$

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

$$18\left(\frac{-x+4}{2\times 3}-2\right)-12x=24$$

Multiply 2 and 3 to get 6.

$$18\left(\frac{-x+4}{6}-2\right)-12x=24$$

Use the distributive property to multiply 18 by \frac{-x+4}{6}-2.

$$18\times \frac{-x+4}{6}-36-12x=24$$

Cancel out 6, the greatest common factor in 18 and 6.

$$3\left(-x+4\right)-36-12x=24$$

Use the distributive property to multiply 3 by -x+4.

$$-3x+12-36-12x=24$$

Subtract 36 from 12 to get -24.

$$-3x-24-12x=24$$

Combine -3x and -12x to get -15x.

$$-15x-24=24$$

Add 24 to both sides.

$$-15x=24+24$$

Add 24 and 24 to get 48.

$$-15x=48$$

Divide both sides by -15.

$$x=\frac{48}{-15}$$

Reduce the fraction \frac{48}{-15} to lowest terms by extracting and canceling out 3.

$$x=-\frac{16}{5}$$