Question

heather is pumping water into a tank at a rate of 16 liters per minute. since she started pumping water, 14 liters has splashed out of the tank. her goal is given by $16x - 14 < 66$, where $x$ is the number of minutes she pumps water into the tank.
complete the parts below.
(a) solve the given inequality and graph the solution on the number line below.
number line from 0 to 30 with tick marks at even numbers and some tools for graphing
(b) choose and complete the statement that best describes the solution.
\\(\circ\\) to meet the goal, the tank will have less than \\(\square\\) liters of water in it. this will take less than \\(\square\\) minutes.
\\(\circ\\) to meet the goal, the tank will have more than \\(\square\\) liters of water in it. this will take less than \\(\square\\) minutes.
\\(\circ\\) to meet the goal, the tank will have less than \\(\square\\) liters of water in it. this will take more than \\(\square\\) minutes.

Explanation:

Step1: Add 14 to both sides

\(16x - 14 + 14 < 66 + 14\)
\(16x < 80\)

Step2: Divide by 16

\(\frac{16x}{16} < \frac{80}{16}\)
\(x < 5\)

Step3: Analyze inequality meaning

Left side \(16x - 14\) is tank water; right side 66. So water < 66 liters, time \(x < 5\) minutes.

Step4: Graph solution

On number line, open circle at 5, arrow left.

Answer:

(a) \(x < 5\)
(b) To meet the goal, the tank will have less than 66 liters of water in it. This will take less than 5 minutes.