Solution Sets of Equations & Inequalities Quick Check
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Question
What value falls in the solution set of the inequality −3(4k+1)<15 ?(1 point)
Responses
−5
negative 5
−32
Start Fraction negative 3 over 2 End Fraction
−4
negative 4
−1
To find the value that falls in the solution set of the inequality −3(4k+1)<15, we can first simplify the inequality:
−3(4k+1) < 15
−12k − 3 < 15
Next, we can isolate the variable by subtracting 3 from both sides:
−12k < 18
Finally, we can solve for k by dividing both sides by -12. Remember to reverse the inequality when dividing by a negative number:
k > -18/12
k > -3/2
So, the value that falls in the solution set of the inequality is -3/2.
To find the value that falls in the solution set of the inequality −3(4k+1) < 15, we need to solve the inequality.
Here are the step-by-step instructions to solve the inequality:
Step 1: Distribute the -3 to each term inside the parentheses:
-3 * 4k = -12k
-3 * 1 = -3
The inequality becomes: -12k - 3 < 15
Step 2: Add 3 to both sides of the inequality to isolate the variable:
-12k - 3 + 3 < 15 + 3
-12k < 18
Step 3: Divide both sides of the inequality by -12. Remember, when dividing or multiplying by a negative number, the inequality sign flips:
-12k / -12 > 18 / -12
k > -1.5
So, the solution set for the inequality −3(4k+1) < 15 is k > -1.5.
Therefore, the value that falls in the solution set of the inequality is any value greater than -1.5.
To find the value that falls in the solution set of the inequality −3(4k+1)<15, we need to solve the inequality for k.
First, let's distribute the -3 to the terms inside the parentheses:
-12k - 3 < 15
Next, let's isolate the variable by moving the constant term to the other side of the inequality:
-12k < 18
Now, divide both sides by -12 to solve for k. Since we are dividing by a negative number, the direction of the inequality symbol will change:
k > 18 / -12
Simplifying the expression on the right:
k > -3/2
So, the value that falls in the solution set of the inequality is any number greater than -3/2.
Among the provided options, the value -1 is the only number that is greater than -3/2. Therefore, the correct answer is -1.