What value falls in the solution set of the inequality -3(4k+1)<15?
-3/2
-4
-5
-1
To find the value that falls in the solution set of the inequality -3(4k+1) < 15, follow these steps:
Step 1: Distribute -3 to the terms inside the parentheses
-12k - 3 < 15
Step 2: Add 3 to both sides of the inequality to isolate the -12k term
-12k - 3 + 3 < 15 + 3
-12k < 18
Step 3: Divide both sides of the inequality by -12. Since we are dividing by a negative number, the direction of the inequality sign reverses.
k > 18 / -12
k > -3/2
Therefore, the value that falls in the solution set of the inequality is k > -3/2.
To find the value that falls in the solution set of the inequality -3(4k+1)<15, you need to solve the inequality by following these steps:
1. Distribute -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. Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign: k > -18/12.
Simplifying -18/12 gives -3/2, or -1.5.
Therefore, the value that falls in the solution set of the inequality -3(4k+1)<15 is k > -3/2 or k > -1.5.
Among the given options, the value that satisfies this inequality is -1, as it is greater than -1.5.
To solve the inequality, let's simplify the left side first:
-3(4k+1) < 15
-12k - 3< 15
Next, let's isolate the variable by adding 3 to both sides:
-12k < 18
Now, divide both sides of the inequality by -12. Since we are dividing by a negative number, the inequality sign flips:
k > -18/12
Simplifying further:
k > -3/2
Therefore, the value that falls in the solution set of the inequality is -3/2.