Solve -x-1/3leqx+1

$$- \frac { x - 1 } { 3 } \leq x + 1$$

Solve for x

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

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$-\left(x-1\right)\leq 3x+3$$

To find the opposite of x-1, find the opposite of each term.

$$-x-\left(-1\right)\leq 3x+3$$

The opposite of -1 is 1.

$$-x+1\leq 3x+3$$

Subtract 3x from both sides.

$$-x+1-3x\leq 3$$

Combine -x and -3x to get -4x.

$$-4x+1\leq 3$$

Subtract 1 from both sides.

$$-4x\leq 3-1$$

Subtract 1 from 3 to get 2.

$$-4x\leq 2$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

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

Reduce the fraction \frac{2}{-4} to lowest terms by extracting and canceling out 2.

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