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

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

Solve for x

$$x = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 2,8,4.

$$4-\left(2x+5\right)=2\left(x+1\right)-16x+24$$

To find the opposite of 2x+5, find the opposite of each term.

$$4-2x-5=2\left(x+1\right)-16x+24$$

Subtract 5 from 4 to get -1.

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

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

$$-1-2x=2x+2-16x+24$$

Combine 2x and -16x to get -14x.

$$-1-2x=-14x+2+24$$

Add 2 and 24 to get 26.

$$-1-2x=-14x+26$$

Add 14x to both sides.

$$-1-2x+14x=26$$

Combine -2x and 14x to get 12x.

$$-1+12x=26$$

Add 1 to both sides.

$$12x=26+1$$

Add 26 and 1 to get 27.

$$12x=27$$

Divide both sides by 12.

$$x=\frac{27}{12}$$

Reduce the fraction \frac{27}{12} to lowest terms by extracting and canceling out 3.

$$x=\frac{9}{4}$$