Question

christine is pumping water into an aquarium at a rate of 12 liters per minute. the aquarium had 36 liters of water in it before she started. her goal is given by \\(12x + 36 < 324\\), 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.\
\\(\circ\\) to meet the goal, the aquarium will have less than \\(\square\\) liters of water in it. this will take more than \\(\square\\) minutes.\
\\(\circ\\) to meet the goal, the aquarium will have more than \\(\square\\) liters of water in it. this will take less than \\(\square\\) minutes.\
\\(\circ\\) to meet the goal, the aquarium will have less than \\(\square\\) liters of water in it. this will take less than \\(\square\\) minutes.

Explanation:

Step1: Subtract 36 from both sides

\(12x + 36 - 36 < 324 - 36\)
\(12x < 288\)

Step2: Divide by 12

\(\frac{12x}{12} < \frac{288}{12}\)
\(x < 24\)

Step3: Interpret inequality for part (b)

Left side of inequality: total water = \(12x + 36\); Right side: 324. So total water < 324 liters. Solution \(x < 24\) means time < 24 minutes.

(Note: For the graph in part (a), place an open circle at 24 on the number line and shade all values to the left of 24.)

Answer:

(a) \(x < 24\); Graph: Open circle at 24, shaded left
(b) To meet the goal, the aquarium will have less than 324 liters of water in it. This will take less than 24 minutes.