Question

Solve the following inequality for k. Write your answer in simplest form. 1 -(-6k + 6) ≤ 3k + 1 + 5k

Answer 1

Given:

1 - (- 6k + 6) ≤ 3k + 1 + 5k

Let's solve the inequality for k.

USe distributive property to expand the parenthesis:

1 + 6k - 6 ≤ 3k + 1 + 5k

Add 6 to both sides:

1 + 6k - 6 + 6 ≤ 3k + 1 + 5k + 6

1 + 6k ≤3k + 5k + 6 + 1

1 + 6k ≤ 3k + 5k + 7

1 + 6k ≤ 8k + 7

Subtract 8k from both sides:

1 + 6k - 8k ≤ 8k - 8k + 7

1 - 2k ≤ 7

Subtract 1 from both sides:

1 - 1 - 2k ≤ 7 - 1

-2k ≤ 6

Divide both sides by -2:

$\begin{gathered} \frac{-2k}{-2}\le\frac{6}{-2} \\ \\ k\ge-3 \end{gathered}$

The inequality sign was flipped because we divided both sides by a negative value. (The inequality sign should only be flipped when you multiply or divide both sides with a negative number)

ANSWER:

k ≥ -3