Solve -4/9u-2leq7/6u+1/9

$$- \frac { 4 } { 9 } u - 2 \leq \frac { 7 } { 6 } u + \frac { 1 } { 9 }$$

Solve for u

$$u\geq -\frac{38}{29}$$

Solution Steps

Subtract \frac{7}{6}u from both sides.

$$-\frac{4}{9}u-2-\frac{7}{6}u\leq \frac{1}{9}$$

Combine -\frac{4}{9}u and -\frac{7}{6}u to get -\frac{29}{18}u.

$$-\frac{29}{18}u-2\leq \frac{1}{9}$$

Add 2 to both sides.

$$-\frac{29}{18}u\leq \frac{1}{9}+2$$

Convert 2 to fraction \frac{18}{9}.

$$-\frac{29}{18}u\leq \frac{1}{9}+\frac{18}{9}$$

Since \frac{1}{9} and \frac{18}{9} have the same denominator, add them by adding their numerators.

$$-\frac{29}{18}u\leq \frac{1+18}{9}$$

Add 1 and 18 to get 19.

$$-\frac{29}{18}u\leq \frac{19}{9}$$

Multiply both sides by -\frac{18}{29}, the reciprocal of -\frac{29}{18}. Since -\frac{29}{18} is negative, the inequality direction is changed.

$$u\geq \frac{19}{9}\left(-\frac{18}{29}\right)$$

Multiply \frac{19}{9} times -\frac{18}{29} by multiplying numerator times numerator and denominator times denominator.

$$u\geq \frac{19\left(-18\right)}{9\times 29}$$

Do the multiplications in the fraction \frac{19\left(-18\right)}{9\times 29}.

$$u\geq \frac{-342}{261}$$

Reduce the fraction \frac{-342}{261} to lowest terms by extracting and canceling out 9.

$$u\geq -\frac{38}{29}$$