Solve x+5/4-2x-3/3=6x-1/8+2x-1/12

$$\frac { x + 5 } { 4 } - \frac { 2 x - 3 } { 3 } = \frac { 6 x - 1 } { 8 } + \frac { 2 x - 1 } { 12 }$$

Solve for x

$$x = \frac{59}{32} = 1\frac{27}{32} = 1.84375$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 4,3,8,12.

$$6\left(x+5\right)-8\left(2x-3\right)=3\left(6x-1\right)+2\left(2x-1\right)$$

Use the distributive property to multiply 6 by x+5.

$$6x+30-8\left(2x-3\right)=3\left(6x-1\right)+2\left(2x-1\right)$$

Use the distributive property to multiply -8 by 2x-3.

$$6x+30-16x+24=3\left(6x-1\right)+2\left(2x-1\right)$$

Combine 6x and -16x to get -10x.

$$-10x+30+24=3\left(6x-1\right)+2\left(2x-1\right)$$

Add 30 and 24 to get 54.

$$-10x+54=3\left(6x-1\right)+2\left(2x-1\right)$$

Use the distributive property to multiply 3 by 6x-1.

$$-10x+54=18x-3+2\left(2x-1\right)$$

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

$$-10x+54=18x-3+4x-2$$

Combine 18x and 4x to get 22x.

$$-10x+54=22x-3-2$$

Subtract 2 from -3 to get -5.

$$-10x+54=22x-5$$

Subtract 22x from both sides.

$$-10x+54-22x=-5$$

Combine -10x and -22x to get -32x.

$$-32x+54=-5$$

Subtract 54 from both sides.

$$-32x=-5-54$$

Subtract 54 from -5 to get -59.

$$-32x=-59$$

Divide both sides by -32.

$$x=\frac{-59}{-32}$$

Fraction \frac{-59}{-32} can be simplified to \frac{59}{32} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{59}{32}$$