Solve 1-x/2-1/4geq1

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

Solve for x

$$x\leq -\frac{3}{2}$$

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.

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

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

$$2-2x-1\geq 4$$

Subtract 1 from 2 to get 1.

$$1-2x\geq 4$$

Subtract 1 from both sides.

$$-2x\geq 4-1$$

Subtract 1 from 4 to get 3.

$$-2x\geq 3$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x\leq -\frac{3}{2}$$