Solve x+5/4-x+1/2=3/4-3/5

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

Solve for x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 4,2,5.

$$20x+25-10\left(x+1\right)=15-12$$

Use the distributive property to multiply -10 by x+1.

$$20x+25-10x-10=15-12$$

Combine 20x and -10x to get 10x.

$$10x+25-10=15-12$$

Subtract 10 from 25 to get 15.

$$10x+15=15-12$$

Subtract 12 from 15 to get 3.

$$10x+15=3$$

Subtract 15 from both sides.

$$10x=3-15$$

Subtract 15 from 3 to get -12.

$$10x=-12$$

Divide both sides by 10.

$$x=\frac{-12}{10}$$

Reduce the fraction \frac{-12}{10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{6}{5}$$