Solve 2x+3/3<x-1/2

$$\frac { 2 x + 3 } { 3 } < \frac { x - 1 } { 2 }$$

Solve for x

$$x<-9$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

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

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

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

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

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

Subtract 3x from both sides.

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

Combine 4x and -3x to get x.

$$x+6<-3$$

Subtract 6 from both sides.

$$x<-3-6$$

Subtract 6 from -3 to get -9.

$$x<-9$$