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

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

Solve for x

$$x = -\frac{11}{5} = -2\frac{1}{5} = -2.2$$

Steps for Solving Linear Equation

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

$$x-5-2\left(x-1\right)=4x+8$$

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

$$x-5-2x+2=4x+8$$

Combine x and -2x to get -x.

$$-x-5+2=4x+8$$

Add -5 and 2 to get -3.

$$-x-3=4x+8$$

Subtract 4x from both sides.

$$-x-3-4x=8$$

Combine -x and -4x to get -5x.

$$-5x-3=8$$

Add 3 to both sides.

$$-5x=8+3$$

Add 8 and 3 to get 11.

$$-5x=11$$

Divide both sides by -5.

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

Fraction \frac{11}{-5} can be rewritten as -\frac{11}{5} by extracting the negative sign.

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