Solve 3(x-1)-2(x+2)<-3(x-1)

$$3 ( x - 1 ) - 2 ( x + 2 ) < - 3 ( x - 1 )$$

Solve for x

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

Solution Steps

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

$$3x-3-2\left(x+2\right)<-3\left(x-1\right)$$

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

$$3x-3-2x-4<-3\left(x-1\right)$$

Combine 3x and -2x to get x.

$$x-3-4<-3\left(x-1\right)$$

Subtract 4 from -3 to get -7.

$$x-7<-3\left(x-1\right)$$

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

$$x-7<-3x+3$$

Add 3x to both sides.

$$x-7+3x<3$$

Combine x and 3x to get 4x.

$$4x-7<3$$

Add 7 to both sides.

$$4x<3+7$$

Add 3 and 7 to get 10.

$$4x<10$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x<\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

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