Solve 1/8w-2leq5w-9/4

$$\frac { 1 } { 8 } w - 2 \leq 5 w - \frac { 9 } { 4 }$$

Solve for w

$$w\geq \frac{2}{39}$$

Solution Steps

Subtract 5w from both sides.

$$\frac{1}{8}w-2-5w\leq -\frac{9}{4}$$

Combine \frac{1}{8}w and -5w to get -\frac{39}{8}w.

$$-\frac{39}{8}w-2\leq -\frac{9}{4}$$

Add 2 to both sides.

$$-\frac{39}{8}w\leq -\frac{9}{4}+2$$

Convert 2 to fraction \frac{8}{4}.

$$-\frac{39}{8}w\leq -\frac{9}{4}+\frac{8}{4}$$

Since -\frac{9}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$-\frac{39}{8}w\leq \frac{-9+8}{4}$$

Add -9 and 8 to get -1.

$$-\frac{39}{8}w\leq -\frac{1}{4}$$

Multiply both sides by -\frac{8}{39}, the reciprocal of -\frac{39}{8}. Since -\frac{39}{8} is negative, the inequality direction is changed.

$$w\geq -\frac{1}{4}\left(-\frac{8}{39}\right)$$

Multiply -\frac{1}{4} times -\frac{8}{39} by multiplying numerator times numerator and denominator times denominator.

$$w\geq \frac{-\left(-8\right)}{4\times 39}$$

Do the multiplications in the fraction \frac{-\left(-8\right)}{4\times 39}.

$$w\geq \frac{8}{156}$$

Reduce the fraction \frac{8}{156} to lowest terms by extracting and canceling out 4.

$$w\geq \frac{2}{39}$$