Solve -5(u-19)leq-6+2u

$$- 5 ( u - 19 ) \leq - 6 + 2 u$$

Solve for u

$$u\geq \frac{101}{7}$$

Solution Steps

Use the distributive property to multiply -5 by u-19.

$$-5u+95\leq -6+2u$$

Subtract 2u from both sides.

$$-5u+95-2u\leq -6$$

Combine -5u and -2u to get -7u.

$$-7u+95\leq -6$$

Subtract 95 from both sides.

$$-7u\leq -6-95$$

Subtract 95 from -6 to get -101.

$$-7u\leq -101$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$u\geq \frac{-101}{-7}$$

Fraction \frac{-101}{-7} can be simplified to \frac{101}{7} by removing the negative sign from both the numerator and the denominator.

$$u\geq \frac{101}{7}$$