Question

for each part below, write an inequality to represent the given statement. then graph the inequality on the number line. (a) the amount of water in a fish tank is between 7 liters and 14 liters, exclusive. use ( a ) for the amount of water in liters. inequality: \\(\square\\) \\(\square<\square\\) \\(\square>\square\\) \\(\square\leq\square\\) \\(\square\geq\square\\) graph: (number line with 1 to 15) (b) the amount of water in a fish tank is 4 liters or more. use ( a ) for the amount of water in liters. inequality: \\(\square\\) \\(\square<\square\\) \\(\square>\square\\) \\(\square\leq\square\\) \\(\square\geq\square\\) graph: (number line with 1 to 15)

Explanation:

Part (a) Step 1: Define the inequality

The amount of water \( a \) is between 7 and 14 liters, exclusive. So \( 7 < a < 14 \).

Part (a) Step 2: Graph the inequality

On the number line, we use open circles at 7 and 14 (since the endpoints are exclusive) and shade the region between them.

Part (b) Step 1: Define the inequality

The amount of water \( a \) is 4 liters or more. So \( a \geq 4 \).

Part (b) Step 2: Graph the inequality

On the number line, we use a closed circle at 4 (since 4 is included) and shade to the right of 4.

Answer:

Part (a)

Inequality: \( 7 < a < 14 \)
Graph: Open circles at 7 and 14, shade between them on the number line (1 - 15 with 7, 8, 9, 10, 11, 12, 13 shaded between 7 and 14).

Part (b)

Inequality: \( a \geq 4 \)
Graph: Closed circle at 4, shade to the right of 4 on the number line (1 - 15 with 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 shaded from 4 onwards).