Solve 1/3w-1/2leq5/6w+1/2

$$\frac { 1 } { 3 } w - \frac { 1 } { 2 } \leq \frac { 5 } { 6 } w + \frac { 1 } { 2 }$$

Solve for w

$$w\geq -2$$

Solution Steps

Subtract \frac{5}{6}w from both sides.

$$\frac{1}{3}w-\frac{1}{2}-\frac{5}{6}w\leq \frac{1}{2}$$

Combine \frac{1}{3}w and -\frac{5}{6}w to get -\frac{1}{2}w.

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

Add \frac{1}{2} to both sides.

$$-\frac{1}{2}w\leq \frac{1}{2}+\frac{1}{2}$$

Since \frac{1}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}w\leq \frac{1+1}{2}$$

Add 1 and 1 to get 2.

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

Divide 2 by 2 to get 1.

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

Multiply both sides by -2, the reciprocal of -\frac{1}{2}. Since -\frac{1}{2} is negative, the inequality direction is changed.

$$w\geq 1\left(-2\right)$$

Multiply 1 and -2 to get -2.

$$w\geq -2$$