Solve 3/2(x-5)-3/2x-3/4[4-(x-2/6)]=frac{5}{8}(x-2)

$$\frac { 3 } { 2 } ( x - 5 ) - \frac { 3 } { 2 } x - \frac { 3 } { 4 } [ 4 - ( \frac { x - 2 } { 6 } ) ] = \frac { 5 } { 8 } ( x - 2 )$$

Solve for x

$$x=-19$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 2,4,6,8.

$$24\left(\frac{3}{2}\left(x-5\right)-\frac{3}{2}x\right)-18\left(4-\frac{x-2}{6}\right)=15\left(x-2\right)$$

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

$$24\left(\frac{3}{2}x+\frac{3}{2}\left(-5\right)-\frac{3}{2}x\right)-18\left(4-\frac{x-2}{6}\right)=15\left(x-2\right)$$

Express \frac{3}{2}\left(-5\right) as a single fraction.

$$24\left(\frac{3}{2}x+\frac{3\left(-5\right)}{2}-\frac{3}{2}x\right)-18\left(4-\frac{x-2}{6}\right)=15\left(x-2\right)$$

Multiply 3 and -5 to get -15.

$$24\left(\frac{3}{2}x+\frac{-15}{2}-\frac{3}{2}x\right)-18\left(4-\frac{x-2}{6}\right)=15\left(x-2\right)$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$24\left(\frac{3}{2}x-\frac{15}{2}-\frac{3}{2}x\right)-18\left(4-\frac{x-2}{6}\right)=15\left(x-2\right)$$

Combine \frac{3}{2}x and -\frac{3}{2}x to get 0.

$$24\left(-\frac{15}{2}\right)-18\left(4-\frac{x-2}{6}\right)=15\left(x-2\right)$$

Express 24\left(-\frac{15}{2}\right) as a single fraction.

$$\frac{24\left(-15\right)}{2}-18\left(4-\frac{x-2}{6}\right)=15\left(x-2\right)$$

Multiply 24 and -15 to get -360.

$$\frac{-360}{2}-18\left(4-\frac{x-2}{6}\right)=15\left(x-2\right)$$

Divide -360 by 2 to get -180.

$$-180-18\left(4-\frac{x-2}{6}\right)=15\left(x-2\right)$$

Use the distributive property to multiply 15 by x-2.

$$-180-18\left(4-\frac{x-2}{6}\right)=15x-30$$

Divide each term of x-2 by 6 to get \frac{1}{6}x-\frac{1}{3}.

$$-180-18\left(4-\left(\frac{1}{6}x-\frac{1}{3}\right)\right)=15x-30$$

To find the opposite of \frac{1}{6}x-\frac{1}{3}, find the opposite of each term.

$$-180-18\left(4-\frac{1}{6}x-\left(-\frac{1}{3}\right)\right)=15x-30$$

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$-180-18\left(4-\frac{1}{6}x+\frac{1}{3}\right)=15x-30$$

Convert 4 to fraction \frac{12}{3}.

$$-180-18\left(\frac{12}{3}-\frac{1}{6}x+\frac{1}{3}\right)=15x-30$$

Since \frac{12}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$-180-18\left(\frac{12+1}{3}-\frac{1}{6}x\right)=15x-30$$

Add 12 and 1 to get 13.

$$-180-18\left(\frac{13}{3}-\frac{1}{6}x\right)=15x-30$$

Use the distributive property to multiply -18 by \frac{13}{3}-\frac{1}{6}x.

$$-180-18\times \frac{13}{3}-18\left(-\frac{1}{6}\right)x=15x-30$$

Express -18\times \frac{13}{3} as a single fraction.

$$-180+\frac{-18\times 13}{3}-18\left(-\frac{1}{6}\right)x=15x-30$$

Multiply -18 and 13 to get -234.

$$-180+\frac{-234}{3}-18\left(-\frac{1}{6}\right)x=15x-30$$

Divide -234 by 3 to get -78.

$$-180-78-18\left(-\frac{1}{6}\right)x=15x-30$$

Express -18\left(-\frac{1}{6}\right) as a single fraction.

$$-180-78+\frac{-18\left(-1\right)}{6}x=15x-30$$

Multiply -18 and -1 to get 18.

$$-180-78+\frac{18}{6}x=15x-30$$

Divide 18 by 6 to get 3.

$$-180-78+3x=15x-30$$

Subtract 78 from -180 to get -258.

$$-258+3x=15x-30$$

Subtract 15x from both sides.

$$-258+3x-15x=-30$$

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

$$-258-12x=-30$$

Add 258 to both sides.

$$-12x=-30+258$$

Add -30 and 258 to get 228.

$$-12x=228$$

Divide both sides by -12.

$$x=\frac{228}{-12}$$

Divide 228 by -12 to get -19.

$$x=-19$$