Solve 2x-3(x-1)+8=3x-2(x+2)

$$2x-3(x-1)+8=3x-2(x+2)$$

Solve for x

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by x-1.

$$2x-3x+3+8=3x-2\left(x+2\right)$$

Combine 2x and -3x to get -x.

$$-x+3+8=3x-2\left(x+2\right)$$

Add 3 and 8 to get 11.

$$-x+11=3x-2\left(x+2\right)$$

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

$$-x+11=3x-2x-4$$

Combine 3x and -2x to get x.

$$-x+11=x-4$$

Subtract x from both sides.

$$-x+11-x=-4$$

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

$$-2x+11=-4$$

Subtract 11 from both sides.

$$-2x=-4-11$$

Subtract 11 from -4 to get -15.

$$-2x=-15$$

Divide both sides by -2.

$$x=\frac{-15}{-2}$$

Fraction \frac{-15}{-2} can be simplified to \frac{15}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{15}{2}$$