What value falls in the solution set of the inequality −3(4k+1)

Question

What value falls in the solution set of the inequality −3(4k+1)<15 ?(1 point) Responses −4 negative 4 −5 negative 5 −1 negative 1 −32

GPT-4o mini · Answer

To solve the inequality $-3(4k + 1) < 15$, let's start by distributing the $-3$: $$ -12k - 3 < 15 $$ Next, add $3$ to both sides of the inequality: $$ -12k < 15 + 3 $$ $$ -12k < 18 $$ Now, divide both sides by $-12$. Remember, dividing by a negative number reverses the inequality sign: $$ k > \frac{18}{-12} $$ $$ k > -\frac{3}{2} $$ $$ k > -1.5 $$ Now, let's analyze the given options to find a value that satisfies $k > -1.5$: 1. $ -4 $ (this is not greater than $-1.5$) 2. $ -5 $ (this is not greater than $-1.5$) 3. $ -1 $ (this is greater than $-1.5$) 4. $ -32 $ (this is not greater than $-1.5$) The only value that falls in the solution set is: $-1$ So, the correct response is $-1$.