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

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

Solve for x

$$x<1$$

Solution Steps

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

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

Combine 3x and 2x to get 5x.

$$5x-3<x+1$$

Subtract x from both sides.

$$5x-3-x<1$$

Combine 5x and -x to get 4x.

$$4x-3<1$$

Add 3 to both sides.

$$4x<1+3$$

Add 1 and 3 to get 4.

$$4x<4$$

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

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

Divide 4 by 4 to get 1.

$$x<1$$