Solve 6(x+1/8-2x-3/16)=3(3/4x-1/4)-3/8(31-2)

$$6 ( \frac { x + 1 } { 8 } - \frac { 2 x - 3 } { 16 } ) = 3 ( 3 / 4 x - 1 / 4 ) - 3 / 8 ( 31 - 2 )$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

$$96\left(\frac{x+1}{8}-\frac{2x-3}{16}\right)=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(31-2\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 16 is 16. Multiply \frac{x+1}{8} times \frac{2}{2}.

$$96\left(\frac{2\left(x+1\right)}{16}-\frac{2x-3}{16}\right)=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(31-2\right)$$

Since \frac{2\left(x+1\right)}{16} and \frac{2x-3}{16} have the same denominator, subtract them by subtracting their numerators.

$$96\times \frac{2\left(x+1\right)-\left(2x-3\right)}{16}=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(31-2\right)$$

Do the multiplications in 2\left(x+1\right)-\left(2x-3\right).

$$96\times \frac{2x+2-2x+3}{16}=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(31-2\right)$$

Combine like terms in 2x+2-2x+3.

$$96\times \frac{5}{16}=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(31-2\right)$$

Express 96\times \frac{5}{16} as a single fraction.

$$\frac{96\times 5}{16}=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(31-2\right)$$

Multiply 96 and 5 to get 480.

$$\frac{480}{16}=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(31-2\right)$$

Divide 480 by 16 to get 30.

$$30=48\left(\frac{3}{4}x-\frac{1}{4}\right)-6\left(31-2\right)$$

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

$$30=48\times \frac{3}{4}x+48\left(-\frac{1}{4}\right)-6\left(31-2\right)$$

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

$$30=\frac{48\times 3}{4}x+48\left(-\frac{1}{4}\right)-6\left(31-2\right)$$

Multiply 48 and 3 to get 144.

$$30=\frac{144}{4}x+48\left(-\frac{1}{4}\right)-6\left(31-2\right)$$

Divide 144 by 4 to get 36.

$$30=36x+48\left(-\frac{1}{4}\right)-6\left(31-2\right)$$

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

$$30=36x+\frac{48\left(-1\right)}{4}-6\left(31-2\right)$$

Multiply 48 and -1 to get -48.

$$30=36x+\frac{-48}{4}-6\left(31-2\right)$$

Divide -48 by 4 to get -12.

$$30=36x-12-6\left(31-2\right)$$

Subtract 2 from 31 to get 29.

$$30=36x-12-6\times 29$$

Multiply 6 and 29 to get 174.

$$30=36x-12-174$$

Subtract 174 from -12 to get -186.

$$30=36x-186$$

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

$$36x-186=30$$

Add 186 to both sides.

$$36x=30+186$$

Add 30 and 186 to get 216.

$$36x=216$$

Divide both sides by 36.

$$x=\frac{216}{36}$$

Divide 216 by 36 to get 6.

$$x=6$$