Question

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charlie is filling up a tank with water for some fish in a pet shop. he needs the tank to have more than 105 liters of water for the fish to survive in it, and less than 165 liters to avoid it being too full. the hose he is using fills the tank with 20 liters of water each minute. the tank already has 65 liters of water in it. let x be the number of minutes he will continue to fill the tank.
(a) find the possible numbers of minutes he will continue to fill the tank. write your answer as a compound inequality solved for x.
(b) on the number line below, graph the solution that represents the possible numbers of minutes he will continue to fill the tank.

Explanation:

Step1: Set up total water inequality

Total water: $65 + 20x$. It must satisfy $105 < 65 + 20x < 165$

Step2: Subtract 65 from all parts

$105 - 65 < 20x < 165 - 65$
$40 < 20x < 100$

Step3: Divide all parts by 20

$\frac{40}{20} < x < \frac{100}{20}$
$2 < x < 5$

Step4: Graph the solution on number line

• Open circle at $x=2$ (since 2 is not included), open circle at $x=5$ (since 5 is not included), shade the region between 2 and 5.

Answer:

(a) $2 < x < 5$
(b) On the number line: Draw an open circle at 2, an open circle at 5, and shade the segment connecting these two points.