Question

What value falls in the solution set of the inequality −3(4k+1)<15 ?(1 point)
Responses

−32
Start Fraction negative 3 over 2 End Fraction

−4
negative 4

−5
negative 5

−1

Answer 1

To solve this inequality, we need to isolate the variable on one side.

First, distribute the -3 to the terms inside the parentheses:
-3(4k + 1) < 15
-12k - 3 < 15

Next, add 3 to both sides to cancel out the -3:
-12k - 3 + 3 < 15 + 3
-12k < 18

Finally, divide both sides by -12, remembering to flip the inequality sign when dividing by a negative number:
k > 18 / -12

Simplifying, we get:
k > -3/2

Therefore, the value that falls in the solution set of the inequality is Start Fraction negative 3 over 2 End Fraction.