Solve x/4-3x-7/5=5/2-2x-1/4

$$\frac { x } { 4 } - \frac { 3 x - 7 } { 5 } = \frac { 5 } { 2 } - \frac { 2 x - 1 } { 4 }$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

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

$$5x-4\left(3x-7\right)=50-5\left(2x-1\right)$$

Use the distributive property to multiply -4 by 3x-7.

$$5x-12x+28=50-5\left(2x-1\right)$$

Combine 5x and -12x to get -7x.

$$-7x+28=50-5\left(2x-1\right)$$

Use the distributive property to multiply -5 by 2x-1.

$$-7x+28=50-10x+5$$

Add 50 and 5 to get 55.

$$-7x+28=55-10x$$

Add 10x to both sides.

$$-7x+28+10x=55$$

Combine -7x and 10x to get 3x.

$$3x+28=55$$

Subtract 28 from both sides.

$$3x=55-28$$

Subtract 28 from 55 to get 27.

$$3x=27$$

Divide both sides by 3.

$$x=\frac{27}{3}$$

Divide 27 by 3 to get 9.

$$x=9$$