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

User Wenli Wan
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1 Answer

5 votes

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} (-2k)/(-2)\le(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

User Sogartar
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7.1k points