What value falls in the solution set of the inequality −3(4k+1)<15?
To find the solution set of the inequality −3(4k+1)<15, let's first simplify the expression:
−3(4k+1)<15
-12k - 3 < 15
Now, let's isolate the variable on one side by adding 3 to both sides of the inequality:
-12k < 18
Finally, divide both sides of the inequality by -12 (remembering to reverse the inequality sign since we are dividing by a negative number):
k > 18/(-12)
k > -3/2
Therefore, any value of k greater than -3/2 falls in the solution set of the inequality.
To find the value that falls in the solution set of the inequality, we need to solve for k. Let's start by simplifying the inequality:
−3(4k+1) < 15
Distribute -3 to (4k+1):
-12k - 3 < 15
Next, let's isolate the variable k by adding 3 to both sides of the inequality:
-12k < 15 + 3
-12k < 18
To further isolate k, divide both sides of the inequality by -12. Remember that when you divide by a negative number, the inequality sign must be flipped:
k > 18 / -12
Simplifying the division:
k > -3/2
Thus, any value of k greater than -3/2 will make the inequality true, so the value that falls in the solution set is any number greater than -3/2.