Solve 1-x-2/2leqx+1/3

$$1 - \frac { x - 2 } { 2 } \leq \frac { x + 1 } { 3 }$$

Solve for x

$$x\geq 2$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$6-3\left(x-2\right)\leq 2\left(x+1\right)$$

Use the distributive property to multiply -3 by x-2.

$$6-3x+6\leq 2\left(x+1\right)$$

Add 6 and 6 to get 12.

$$12-3x\leq 2\left(x+1\right)$$

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

$$12-3x\leq 2x+2$$

Subtract 2x from both sides.

$$12-3x-2x\leq 2$$

Combine -3x and -2x to get -5x.

$$12-5x\leq 2$$

Subtract 12 from both sides.

$$-5x\leq 2-12$$

Subtract 12 from 2 to get -10.

$$-5x\leq -10$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq \frac{-10}{-5}$$

Divide -10 by -5 to get 2.

$$x\geq 2$$