Solve -7/6w-1leq3/8w+5/6

$$- \frac { 7 } { 6 } w - 1 \leq \frac { 3 } { 8 } w + \frac { 5 } { 6 }$$

Solve for w

$$w\geq -\frac{44}{37}$$

Solution Steps

Subtract \frac{3}{8}w from both sides.

$$-\frac{7}{6}w-1-\frac{3}{8}w\leq \frac{5}{6}$$

Combine -\frac{7}{6}w and -\frac{3}{8}w to get -\frac{37}{24}w.

$$-\frac{37}{24}w-1\leq \frac{5}{6}$$

Add 1 to both sides.

$$-\frac{37}{24}w\leq \frac{5}{6}+1$$

Convert 1 to fraction \frac{6}{6}.

$$-\frac{37}{24}w\leq \frac{5}{6}+\frac{6}{6}$$

Since \frac{5}{6} and \frac{6}{6} have the same denominator, add them by adding their numerators.

$$-\frac{37}{24}w\leq \frac{5+6}{6}$$

Add 5 and 6 to get 11.

$$-\frac{37}{24}w\leq \frac{11}{6}$$

Multiply both sides by -\frac{24}{37}, the reciprocal of -\frac{37}{24}. Since -\frac{37}{24} is negative, the inequality direction is changed.

$$w\geq \frac{11}{6}\left(-\frac{24}{37}\right)$$

Multiply \frac{11}{6} times -\frac{24}{37} by multiplying numerator times numerator and denominator times denominator.

$$w\geq \frac{11\left(-24\right)}{6\times 37}$$

Do the multiplications in the fraction \frac{11\left(-24\right)}{6\times 37}.

$$w\geq \frac{-264}{222}$$

Reduce the fraction \frac{-264}{222} to lowest terms by extracting and canceling out 6.

$$w\geq -\frac{44}{37}$$