Solve x-2/2-x+1/6+7/3=x+3/4

$$\frac { x - 2 } { 2 } - \frac { x + 1 } { 6 } + \frac { 7 } { 3 } = x + \frac { 3 } { 4 }$$

Solve for x

$$x=\frac{5}{8}=0.625$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,6,3,4.

$$6\left(x-2\right)-2\left(x+1\right)+28=12x+9$$

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

$$6x-12-2\left(x+1\right)+28=12x+9$$

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

$$6x-12-2x-2+28=12x+9$$

Combine 6x and -2x to get 4x.

$$4x-12-2+28=12x+9$$

Subtract 2 from -12 to get -14.

$$4x-14+28=12x+9$$

Add -14 and 28 to get 14.

$$4x+14=12x+9$$

Subtract 12x from both sides.

$$4x+14-12x=9$$

Combine 4x and -12x to get -8x.

$$-8x+14=9$$

Subtract 14 from both sides.

$$-8x=9-14$$

Subtract 14 from 9 to get -5.

$$-8x=-5$$

Divide both sides by -8.

$$x=\frac{-5}{-8}$$

Fraction \frac{-5}{-8} can be simplified to \frac{5}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{8}$$