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

$$x=-8$$

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, subtract them by subtracting 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 -48.

$$3x-48-12x=24$$

Combine 3x and -12x to get -9x.

$$-9x-48=24$$

Add 48 to both sides.

$$-9x=24+48$$

Add 24 and 48 to get 72.

$$-9x=72$$

Divide both sides by -9.

$$x=\frac{72}{-9}$$

Divide 72 by -9 to get -8.

$$x=-8$$