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

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

Solve for x

$$x<-\frac{9}{2}$$

Solution Steps

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

$$3x+6<2\left(x-2\right)-\left(x-1\right)$$

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

$$3x+6<2x-4-\left(x-1\right)$$

To find the opposite of x-1, find the opposite of each term.

$$3x+6<2x-4-x-\left(-1\right)$$

The opposite of -1 is 1.

$$3x+6<2x-4-x+1$$

Combine 2x and -x to get x.

$$3x+6<x-4+1$$

Add -4 and 1 to get -3.

$$3x+6<x-3$$

Subtract x from both sides.

$$3x+6-x<-3$$

Combine 3x and -x to get 2x.

$$2x+6<-3$$

Subtract 6 from both sides.

$$2x<-3-6$$

Subtract 6 from -3 to get -9.

$$2x<-9$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x<-\frac{9}{2}$$