Solve =(x+1/8-2x-3/16)=3(3/4x-1/4)-frac{3}{8}(3x-2)

$$= ( \frac { x + 1 } { 8 } - \frac { 2 x - 3 } { 16 } ) = 3 ( \frac { 3 } { 4 } x - \frac { 1 } { 4 } ) - \frac { 3 } { 8 } ( 3 x - 2 )$$

Solve for x

$$x=\frac{5}{18}\approx 0.277777778$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 16, the least common multiple of 8,16,4.

$$2\left(x+1\right)-\left(2x-3\right)=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(3x-2\right)$$

Use the distributive property to multiply 2 by x+1.

$$2x+2-\left(2x-3\right)=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(3x-2\right)$$

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

$$2x+2-2x-\left(-3\right)=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(3x-2\right)$$

The opposite of -3 is 3.

$$2x+2-2x+3=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(3x-2\right)$$

Combine 2x and -2x to get 0.

$$2+3=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(3x-2\right)$$

Add 2 and 3 to get 5.

$$5=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(3x-2\right)$$

Use the distributive property to multiply 48 by \frac{3}{4}x-\frac{1}{4}.

$$5=48\times \frac{3}{4}x+48\left(-\frac{1}{4}\right)-6\left(3x-2\right)$$

Express 48\times \frac{3}{4} as a single fraction.

$$5=\frac{48\times 3}{4}x+48\left(-\frac{1}{4}\right)-6\left(3x-2\right)$$

Multiply 48 and 3 to get 144.

$$5=\frac{144}{4}x+48\left(-\frac{1}{4}\right)-6\left(3x-2\right)$$

Divide 144 by 4 to get 36.

$$5=36x+48\left(-\frac{1}{4}\right)-6\left(3x-2\right)$$

Express 48\left(-\frac{1}{4}\right) as a single fraction.

$$5=36x+\frac{48\left(-1\right)}{4}-6\left(3x-2\right)$$

Multiply 48 and -1 to get -48.

$$5=36x+\frac{-48}{4}-6\left(3x-2\right)$$

Divide -48 by 4 to get -12.

$$5=36x-12-6\left(3x-2\right)$$

Use the distributive property to multiply -6 by 3x-2.

$$5=36x-12-18x+12$$

Combine 36x and -18x to get 18x.

$$5=18x-12+12$$

Add -12 and 12 to get 0.

$$5=18x$$

Swap sides so that all variable terms are on the left hand side.

$$18x=5$$

Divide both sides by 18.

$$x=\frac{5}{18}$$