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

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

Solve for x

$$x = \frac{17}{4} = 4\frac{1}{4} = 4.25$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 5 by x+1.

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

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

$$5x+5-4x+2=5x-10$$

Combine 5x and -4x to get x.

$$x+5+2=5x-10$$

Add 5 and 2 to get 7.

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

Subtract 5x from both sides.

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

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

$$-4x+7=-10$$

Subtract 7 from both sides.

$$-4x=-10-7$$

Subtract 7 from -10 to get -17.

$$-4x=-17$$

Divide both sides by -4.

$$x=\frac{-17}{-4}$$

Fraction \frac{-17}{-4} can be simplified to \frac{17}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{17}{4}$$