Question

for each part below, write an inequality to represent the given statement. then graph the inequality on the number line.
(a) the highest temperature recorded for a day is between 6 degrees celsius and 15 degrees celsius, inclusive. use t for the temperature in degrees celsius.
inequality:
options: □<□, □>□, □≤□, □≥□
graph:
number line from 1 to 15 with marking tools: open circle, closed circle, arrow

Explanation:

Step1: Understand the statement

The temperature \( t \) is between 6 and 15 degrees Celsius, inclusive. This means \( t \) is greater than or equal to 6 and less than or equal to 15.

Step2: Write the inequality

Combining these two conditions, we get the compound inequality \( 6 \leq t \leq 15 \).

To graph this inequality on the number line:

• We use a closed circle (filled dot) at 6 and 15 because the inequality is inclusive ( \( \leq \) and \( \geq \) ).
• Then we draw a line segment connecting the two closed circles to represent all the values of \( t \) between 6 and 15, including 6 and 15.

Answer:

Inequality: \( 6 \leq t \leq 15 \)

For the graph:

• Place a closed dot (filled circle) at 6 and 15 on the number line.
• Draw a line connecting the two closed dots to show all values of \( t \) between 6 and 15, including 6 and 15.