Solve x/4-1/2leqx/2+1

$$\frac { x } { 4 } - \frac { 1 } { 2 } \leq \frac { x } { 2 } + 1$$

Solve for x

$$x\geq -6$$

Solution Steps

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

$$x-2\leq 2x+4$$

Subtract 2x from both sides.

$$x-2-2x\leq 4$$

Combine x and -2x to get -x.

$$-x-2\leq 4$$

Add 2 to both sides.

$$-x\leq 4+2$$

Add 4 and 2 to get 6.

$$-x\leq 6$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\geq -6$$