Question

heather is pumping water into an aquarium at a rate of 13 liters per minute. the aquarium had 25 liters of water in it before she started. her goal is given by $13x + 25 leq 298$, where x is the number of minutes she pumps water into the aquarium. complete the parts below. (a) solve the given inequality and graph the solution on the number line below. (b) choose and complete the statement that best describes the solution. o to meet the goal, the aquarium will have at least liters of water in it. this will take at most minutes. o to meet the goal, the aquarium will have at most liters of water in it. this will take at least minutes. o to meet the goal, the aquarium will have at most liters of water in it. this will take at most minutes.

Explanation:

Step1: Solve the inequality

Subtract 25 from both sides of \(13x + 25\leq298\).
\(13x+25 - 25\leq298 - 25\)
\(13x\leq273\)
Divide both sides by 13.
\(x\leq\frac{273}{13}\)
\(x\leq21\)

Step2: Analyze the statement

The inequality \(13x + 25\leq298\) means the amount of water (\(13x + 25\)) is at most 298 liters. And \(x\leq21\) means the time \(x\) (number of minutes) is at most 21 minutes.

Answer:

(a) The solution of the inequality \(13x + 25\leq298\) is \(x\leq21\). On the number - line, we put a closed circle at 21 (since \(x = 21\) is included in the solution) and shade to the left.
(b) To meet the goal, the aquarium will have at most 298 liters of water in it. This will take at most 21 minutes.