Solve x+5/6-[14-x/2-1/4]=2x-7/12

$$\frac { x + 5 } { 6 } - [ \frac { 14 - x } { 2 } - \frac { 1 } { 4 } ] = \frac { 2 x - 7 } { 12 }$$

Solve for x

$$x = \frac{32}{3} = 10\frac{2}{3} \approx 10.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 6,2,4,12.

$$2\left(x+5\right)-12\left(\frac{14-x}{2}-\frac{1}{4}\right)=2x-7$$

Use the distributive property to multiply 2 by x+5.

$$2x+10-12\left(\frac{14-x}{2}-\frac{1}{4}\right)=2x-7$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{14-x}{2} times \frac{2}{2}.

$$2x+10-12\left(\frac{2\left(14-x\right)}{4}-\frac{1}{4}\right)=2x-7$$

Since \frac{2\left(14-x\right)}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$2x+10-12\times \frac{2\left(14-x\right)-1}{4}=2x-7$$

Do the multiplications in 2\left(14-x\right)-1.

$$2x+10-12\times \frac{28-2x-1}{4}=2x-7$$

Combine like terms in 28-2x-1.

$$2x+10-12\times \frac{27-2x}{4}=2x-7$$

Cancel out 4, the greatest common factor in 12 and 4.

$$2x+10-3\left(27-2x\right)=2x-7$$

Use the distributive property to multiply -3 by 27-2x.

$$2x+10-81+6x=2x-7$$

Subtract 81 from 10 to get -71.

$$2x-71+6x=2x-7$$

Combine 2x and 6x to get 8x.

$$8x-71=2x-7$$

Subtract 2x from both sides.

$$8x-71-2x=-7$$

Combine 8x and -2x to get 6x.

$$6x-71=-7$$

Add 71 to both sides.

$$6x=-7+71$$

Add -7 and 71 to get 64.

$$6x=64$$

Divide both sides by 6.

$$x=\frac{64}{6}$$

Reduce the fraction \frac{64}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{32}{3}$$