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

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

Solve for x

$$x = \frac{21}{2} = 10\frac{1}{2} = 10.5$$

Steps for Solving Linear Equation

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

$$5\left(2x+3\right)-2\left(x+2\right)=10x-10$$

Use the distributive property to multiply 5 by 2x+3.

$$10x+15-2\left(x+2\right)=10x-10$$

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

$$10x+15-2x-4=10x-10$$

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

$$8x+15-4=10x-10$$

Subtract 4 from 15 to get 11.

$$8x+11=10x-10$$

Subtract 10x from both sides.

$$8x+11-10x=-10$$

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

$$-2x+11=-10$$

Subtract 11 from both sides.

$$-2x=-10-11$$

Subtract 11 from -10 to get -21.

$$-2x=-21$$

Divide both sides by -2.

$$x=\frac{-21}{-2}$$

Fraction \frac{-21}{-2} can be simplified to \frac{21}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{21}{2}$$