Question

salma is pumping water into an aquarium at a rate of 11 liters per minute. the aquarium had 41 liters of water in it before she started. her goal is given by 11x + 41 ≤ 250, 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. (number line with 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30 and graphing tools) (b) choose and complete the statement that best describes the solution. to meet the goal, the aquarium will have at least liters of water in it. this will take at most minutes. to meet the goal, the aquarium will have at most liters of water in it. this will take at least minutes. to meet the goal, the aquarium will have at most liters of water in it. this will take at most minutes.

Explanation:

Step1: Subtract 41 from both sides

\(11x + 41 - 41 \leq 250 - 41\)
\(11x \leq 209\)

Step2: Divide both sides by 11

\(\frac{11x}{11} \leq \frac{209}{11}\)
\(x \leq 19\)

Step3: Analyze the inequality for part (b)

The left side \(11x + 41\) is the total water, so \(11x + 41 \leq 250\) means total water ≤ 250 liters. The solution \(x \leq 19\) means time ≤ 19 minutes. Thus, the correct statement is the third option (assuming the third option in the original is "at most 250 liters... at most 19 minutes").

For the graph in (a): Plot a closed circle at 19 on the number line and shade to the left.

Answer:

(a) \(x \leq 19\)
(b) To meet the goal, the aquarium will have at most 250 liters of water in it. This will take at most 19 minutes.