What value falls in the solution set of the inequality −3(4k+1)<15 ?(1 point)
To solve the inequality, we will isolate the variable k by performing the necessary operations.
−3(4k + 1) < 15
Expanding the left side:
-12k - 3 < 15
Adding 3 to both sides:
-12k < 18
Dividing both sides by -12 and reversing the inequality:
k > -18/12
Simplifying the fraction:
k > -3/2
Therefore, any value of k greater than -3/2 falls in the solution set of the inequality.
To solve the inequality −3(4k+1)<15, we will follow these steps:
1. Distribute the -3 to both terms inside the parentheses:
-12k - 3 < 15
2. Add 3 to both sides of the inequality to isolate the variable:
-12k < 18
3. Divide both sides of the inequality by -12. Note that when dividing by a negative number, the direction of the inequality gets flipped:
k > -18/12
4. Simplify the fraction:
k > -3/2
So, the solution set for the inequality is k > -3/2.
To find the value that falls in the solution set of the inequality −3(4k+1) < 15, we can begin by simplifying the inequality:
−3(4k+1) < 15
First, distribute the -3 to both terms within the parentheses:
-12k - 3 < 15
Next, add 3 to both sides of the inequality to isolate the variable term:
-12k - 3 + 3 < 15 + 3
-12k < 18
Divide both sides of the inequality by -12. Remember, when multiplying or dividing by a negative number, flip the direction of the inequality symbol:
k > 18 / -12
Simplifying further:
k > -3/2
Therefore, the value that falls in the solution set of the inequality −3(4k+1) < 15 is any value of k greater than -3/2.