Solve x+7/4-x+1/5=x+1/10-x+1/2

$$\frac { x + 7 } { 4 } - \frac { x + 1 } { 5 } = \frac { x + 1 } { 10 } - \frac { x + 1 } { 2 }$$

Solve for x

$$x = -\frac{13}{3} = -4\frac{1}{3} \approx -4.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 4,5,10,2.

$$5\left(x+7\right)-4\left(x+1\right)=2\left(x+1\right)-10\left(x+1\right)$$

Use the distributive property to multiply 5 by x+7.

$$5x+35-4\left(x+1\right)=2\left(x+1\right)-10\left(x+1\right)$$

Use the distributive property to multiply -4 by x+1.

$$5x+35-4x-4=2\left(x+1\right)-10\left(x+1\right)$$

Combine 5x and -4x to get x.

$$x+35-4=2\left(x+1\right)-10\left(x+1\right)$$

Subtract 4 from 35 to get 31.

$$x+31=2\left(x+1\right)-10\left(x+1\right)$$

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

$$x+31=2x+2-10\left(x+1\right)$$

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

$$x+31=2x+2-10x-10$$

Combine 2x and -10x to get -8x.

$$x+31=-8x+2-10$$

Subtract 10 from 2 to get -8.

$$x+31=-8x-8$$

Add 8x to both sides.

$$x+31+8x=-8$$

Combine x and 8x to get 9x.

$$9x+31=-8$$

Subtract 31 from both sides.

$$9x=-8-31$$

Subtract 31 from -8 to get -39.

$$9x=-39$$

Divide both sides by 9.

$$x=\frac{-39}{9}$$

Reduce the fraction \frac{-39}{9} to lowest terms by extracting and canceling out 3.

$$x=-\frac{13}{3}$$