Solve x-1/2-xleq1-x/4

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

Solve for x

$$x\geq -3$$

Solution Steps

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

$$2\left(x-1\right)-4x\leq 1-x$$

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

$$2x-2-4x\leq 1-x$$

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

$$-2x-2\leq 1-x$$

Add x to both sides.

$$-2x-2+x\leq 1$$

Combine -2x and x to get -x.

$$-x-2\leq 1$$

Add 2 to both sides.

$$-x\leq 1+2$$

Add 1 and 2 to get 3.

$$-x\leq 3$$

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

$$x\geq -3$$