Solve x+3/4-x-1/6<1

$$\frac { x + 3 } { 4 } - \frac { x - 1 } { 6 } < 1$$

Solve for x

$$x<1$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,6. Since 12 is positive, the inequality direction remains the same.

$$3\left(x+3\right)-2\left(x-1\right)<12$$

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

$$3x+9-2\left(x-1\right)<12$$

Use the distributive property to multiply -2 by x-1.

$$3x+9-2x+2<12$$

Combine 3x and -2x to get x.

$$x+9+2<12$$

Add 9 and 2 to get 11.

$$x+11<12$$

Subtract 11 from both sides.

$$x<12-11$$

Subtract 11 from 12 to get 1.

$$x<1$$