Solve -2(-7k-22)+83kleq100k+74

$$- 2 ( - 7 k - 22 ) + 83 k \leq 100 k + 74$$

Solve for k

$$k\geq -10$$

Solution Steps

Use the distributive property to multiply -2 by -7k-22.

$$14k+44+83k\leq 100k+74$$

Combine 14k and 83k to get 97k.

$$97k+44\leq 100k+74$$

Subtract 100k from both sides.

$$97k+44-100k\leq 74$$

Combine 97k and -100k to get -3k.

$$-3k+44\leq 74$$

Subtract 44 from both sides.

$$-3k\leq 74-44$$

Subtract 44 from 74 to get 30.

$$-3k\leq 30$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$k\geq \frac{30}{-3}$$

Divide 30 by -3 to get -10.

$$k\geq -10$$