Question

write the sentence as an inequality. a number p is less than 6 and greater than 2. inequality: 2 < p < 6 ✔️ graph the inequality.

Explanation:

Step1: Analyze "greater than 2"

The phrase "a number \( p \) is greater than 2" translates to \( 2 < p \) (since \( p \) is larger than 2, the inequality sign opens towards \( p \)).

Step2: Analyze "less than 6"

The phrase "a number \( p \) is less than 6" translates to \( p < 6 \) (since \( p \) is smaller than 6, the inequality sign opens towards 6).

Step3: Combine the inequalities

To represent "a number \( p \) is less than 6 and greater than 2", we combine the two inequalities from Step 1 and Step 2. This gives us the compound inequality \( 2 < p < 6 \).

For graphing the inequality \( 2 < p < 6 \):

• Since \( p \) is greater than 2 (not equal to 2), we use an open circle at 2 on the number line.
• Since \( p \) is less than 6 (not equal to 6), we use an open circle at 6 on the number line.
• Then we draw a line segment connecting the open circles at 2 and 6 to represent all the numbers \( p \) that satisfy both inequalities (i.e., all numbers between 2 and 6, not including 2 and 6 themselves).

Answer:

The inequality is \( 2 < p < 6 \). For the graph, there are open circles at 2 and 6 on the number line, with a line segment connecting them to represent the solution set of \( p \) (all real numbers between 2 and 6, excluding 2 and 6).