Question

your answer is incorrect.
keisha is filling up a tank with water for some fish in a pet shop. she needs the tank to have more than 130 liters of water for the fish to survive in it, and less than 230 liters to avoid it being too full. the hose she is using fills the tank with 25 liters of water each minute. the tank already has 30 liters of water in it. let x be the number of minutes she will continue to fill the tank.
(a) find the possible numbers of minutes she will continue to fill the tank. write your answer as a compound inequality solved for x.
4 ≤ x ≤ 8
(b) on the number line below, graph the solution that represents the possible numbers of minutes she will continue to fill the tank.

Explanation:

Step1: Define total water equation

Total water: $30 + 25x$

Step2: Set lower bound inequality

More than 130 liters:
$30 + 25x > 130$
$25x > 130 - 30$
$25x > 100$
$x > 4$

Step3: Set upper bound inequality

Less than 230 liters:
$30 + 25x < 230$
$25x < 230 - 30$
$25x < 200$
$x < 8$

Step4: Combine into compound inequality

Combine the two results: $4 < x < 8$

Step5: Explain number line graph

Open circles at 4 and 8, shade between them (since x is strictly greater than 4 and strictly less than 8, not equal).

Answer:

(a) $4 < x < 8$
(b) On the number line, draw open circles at the points labeled 4 and 8, then shade the region between these two open circles.