Solve x/2+5/2x+12<x+18

$$\frac { x } { 2 } + \frac { 5 } { 2 } x + 12 < x + 18$$

Solve for x

$$x<3$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$x+5x+24<2x+36$$

Combine x and 5x to get 6x.

$$6x+24<2x+36$$

Subtract 2x from both sides.

$$6x+24-2x<36$$

Combine 6x and -2x to get 4x.

$$4x+24<36$$

Subtract 24 from both sides.

$$4x<36-24$$

Subtract 24 from 36 to get 12.

$$4x<12$$

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

$$x<\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$x<3$$