Unpack inequality: multiply -7.5 in (k-4.2), subtract 31.5 from both sides, divide by -7.5 (flip sign). Solution: k ≥ 0.2.
1. Distribute the terms:
Multiply -7.5 inside the parentheses on the right side of the inequality:
30 ≥ -7.5(k - 4.2)
30 ≥ -7.5k + 31.5
2. Isolate the variable:
To isolate k, let's manipulate the inequality to have k by itself:
Subtract 31.5 from both sides:
30 - 31.5 ≥ -7.5k + 31.5 - 31.5
-1.5 ≥ -7.5k
Divide both sides by -7.5 (remember to flip the inequality sign when dividing by a negative number):
-1.5 / -7.5 ≤ k
0.2 ≥ k
3. Interpret the answer:
The final inequality tells us that k must be greater than or equal to 0.2. In other words, any value of k that is 0.2 or greater satisfies the original inequality.
Complete question below:
Let's solve the inequality: 30≥−7.5(k−4.2)