Solve 4(x-2)=-5(x-1)+3x+2

$$4 ( x - 2 ) = - 5 ( x - 1 ) + 3 x + 2$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by x-2.

$$4x-8=-5\left(x-1\right)+3x+2$$

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

$$4x-8=-5x+5+3x+2$$

Combine -5x and 3x to get -2x.

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

Add 5 and 2 to get 7.

$$4x-8=-2x+7$$

Add 2x to both sides.

$$4x-8+2x=7$$

Combine 4x and 2x to get 6x.

$$6x-8=7$$

Add 8 to both sides.

$$6x=7+8$$

Add 7 and 8 to get 15.

$$6x=15$$

Divide both sides by 6.

$$x=\frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$x=\frac{5}{2}$$