Solve x+1/3-x-1/4geq1/2

$$\frac { x + 1 } { 3 } - \frac { x - 1 } { 4 } \geq \frac { 1 } { 2 }$$

Solve for x

$$x\geq -1$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,4,2. Since 12 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply 4 by x+1.

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

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

$$4x+4-3x+3\geq 6$$

Combine 4x and -3x to get x.

$$x+4+3\geq 6$$

Add 4 and 3 to get 7.

$$x+7\geq 6$$

Subtract 7 from both sides.

$$x\geq 6-7$$

Subtract 7 from 6 to get -1.

$$x\geq -1$$