Solve x-1/-1leqx-2/-2

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

Solve for x

$$x\geq 0$$

Solution Steps

Multiply both sides of the equation by 2, the least common multiple of -1,-2. Since 2 is positive, the inequality direction remains the same.

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

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

$$-2x+2\leq -\left(x-2\right)$$

To find the opposite of x-2, find the opposite of each term.

$$-2x+2\leq -x-\left(-2\right)$$

The opposite of -2 is 2.

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

Add x to both sides.

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

Combine -2x and x to get -x.

$$-x+2\leq 2$$

Subtract 2 from both sides.

$$-x\leq 2-2$$

Subtract 2 from 2 to get 0.

$$-x\leq 0$$

Product of two numbers is ≤0 if one is ≥0 and the other is ≤0. Since -1\leq 0, x must be ≥0.

$$x\geq 0$$