Solve 5x-8/4+5/4=2x-5/3-5x-8/4-frac{2}{8}

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

Solve for x

$$x=\frac{5}{11}\approx 0.454545455$$

Steps for Solving Linear Equation

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

$$6\left(5x-8\right)+30=8\left(2x-5\right)-6\left(5x-8\right)-3\times 2$$

Use the distributive property to multiply 6 by 5x-8.

$$30x-48+30=8\left(2x-5\right)-6\left(5x-8\right)-3\times 2$$

Add -48 and 30 to get -18.

$$30x-18=8\left(2x-5\right)-6\left(5x-8\right)-3\times 2$$

Use the distributive property to multiply 8 by 2x-5.

$$30x-18=16x-40-6\left(5x-8\right)-3\times 2$$

Use the distributive property to multiply -6 by 5x-8.

$$30x-18=16x-40-30x+48-3\times 2$$

Combine 16x and -30x to get -14x.

$$30x-18=-14x-40+48-3\times 2$$

Add -40 and 48 to get 8.

$$30x-18=-14x+8-3\times 2$$

Multiply -3 and 2 to get -6.

$$30x-18=-14x+8-6$$

Subtract 6 from 8 to get 2.

$$30x-18=-14x+2$$

Add 14x to both sides.

$$30x-18+14x=2$$

Combine 30x and 14x to get 44x.

$$44x-18=2$$

Add 18 to both sides.

$$44x=2+18$$

Add 2 and 18 to get 20.

$$44x=20$$

Divide both sides by 44.

$$x=\frac{20}{44}$$

Reduce the fraction \frac{20}{44} to lowest terms by extracting and canceling out 4.

$$x=\frac{5}{11}$$