Question

yolanda is pumping water into an aquarium at a rate of 11 liters per minute. the aquarium had 34 liters of water in it before she started. her goal is given by $11x + 34 < 254$, 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. to meet the goal, the aquanum will have more than liters of water in it. this will take less than minutes. to meet the goal, the aquarium will have less than liters of water in it. this will take less than minutes. to meet the goal, the aquarium will have less than liters of water in it. this will take more than minutes.

Explanation:

Step1: Solve the inequality

Given \(11x + 34<254\).
Subtract 34 from both sides:
\(11x+34 - 34<254 - 34\)
\(11x<220\)
Divide both sides by 11:
\(x < \frac{220}{11}\)
\(x<20\)

Step2: Graph the solution

On the number - line, since \(x < 20\), we use an open circle at \(x = 20\) (because \(x\) is not equal to 20) and draw an arrow to the left.

Step3: Analyze part (b)

The inequality \(11x + 34<254\) means the amount of water \(11x + 34\) (total water in the aquarium) is less than 254 liters. And we found \(x<20\) (the number of minutes is less than 20).

Answer:

(a) The solution of the inequality \(11x + 34<254\) is \(x<20\). On the number - line, place an open circle at 20 and draw an arrow to the left.
(b) To meet the goal, the aquarium will have less than \(254\) liters of water in it. This will take less than \(20\) minutes.