What value falls in the solution set of the inequality −3(4k+1)<15?(1 point)
Responses
−4
−5
−32
−1
To solve the inequality, we will divide both sides by -3, being careful to reverse the inequality sign since we are dividing by a negative number.
−3(4k+1) < 15
Dividing both sides by -3:
4k + 1 > -5
Now, subtracting 1 from both sides:
4k > -6
Finally, dividing both sides by 4:
k > -6/4
Simplifying:
k > -3/2
Therefore, the values that fall in the solution set of the inequality are greater than -3/2.
Among the given options, the only value that satisfies this condition is -1.
Therefore, the correct answer is -1.
To solve the inequality −3(4k+1) < 15, we can start by distributing the -3:
-12k - 3 < 15
Next, let's isolate the term with k by adding 3 to both sides:
-12k < 18
Then, divide both sides by -12. Remember that when dividing by a negative number, we need to reverse the direction of the inequality:
k > -18/12
Simplifying further:
k > -3/2
Therefore, the value that falls in the solution set of the inequality is any number greater than -3/2. So, the correct answer is -1.