Question

Solve for k.

-6 ≤ -2k + 4 ≤ 2.
a) 5 ≤ k ≤ 1
b) k ≥ 1
c) 1 ≤ k ≤ 5
d) 5 ≥ k ≥ 1

Answer 1

To solve the compound inequality -6 ≤ -2k + 4 ≤ 2, we subtract 4 and then divide by -2. The solution is 1 ≤ k ≤ 5, which aligns with option (c).

Step-by-step explanation:

To solve for k in the inequality -6 ≤ -2k + 4 ≤ 2, we need to isolate k by performing the same operations on all three parts of the inequality. First, subtract 4 from all parts to get:

-10 ≤ -2k ≤ -2

Next, divide all parts by -2, remembering to reverse the inequality signs because we are dividing by a negative number:

5 ≥ k ≥ 1

So, the solution is 1 ≤ k ≤ 5, which corresponds to option (c).