The inequality given is: k + 2(k + 1) -(7k + 8)

Let's solve it step by step:

Step 1: Simplify the left side of the inequality by distributing the 2 in 2(k + 1):
k + 2k + 2 -(7k + 8)

Step 2: Combine like terms on the left side:
3k + 2 -(7k + 8)

Step 3: Distribute the negative sign on the right side of the inequality:
3k + 2 -7k - 8

Step 4: Add 7k to both sides to get all k terms on one side:
3k + 7k + 2 -8

Step 5: Combine like terms on the left side:
10k + 2 -8

Step 6: Subtract 2 from both sides to isolate the k term:
10k -10

Step 7: Divide both sides by 10 to solve for k:
k -1

So, the solution to the inequality is k -1.

Question

The inequality given is: k + 2(k + 1) > -(7k + 8)

Let's solve it step by step:

Step 1: Simplify the left side of the inequality by distributing the 2 in 2(k + 1):
k + 2k + 2 > -(7k + 8)

Step 2: Combine like terms on the left side:
3k + 2 > -(7k + 8)

Step 3: Distribute the negative sign on the right side of the inequality:
3k + 2 > -7k - 8

Step 4: Add 7k to both sides to get all k terms on one side:
3k + 7k + 2 > -8

Step 5: Combine like terms on the left side:
10k + 2 > -8

Step 6: Subtract 2 from both sides to isolate the k term:
10k > -10

Step 7: Divide both sides by 10 to solve for k:
k > -1

So, the solution to the inequality is k > -1.

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