Question

graph the solution set of the inequality, where x is an integer, on the number line.

\\-3x \le 21\\

choose the correct graph below.

Explanation:

Solve the inequality

Using the Solving Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Apply the integer constraint

The problem specifies that \(x\) must be an integer. Therefore, the solution set consists only of discrete integer values:

$$ x \in \{-7, -6, -5, -4, \dots\} $$

Identify the correct graph

• Graphs A, B, C, and D show continuous intervals (shaded lines/rays), which represent real number solutions.
• Graphs E and F show discrete points (dots on integers).
• Graph E shows dots at \(\dots, -10, -9, -8, -7\), which corresponds to \(x \le -7\).
• Graph F shows dots at \(-7, -6, -5, -4, \dots\), which corresponds to \(x \ge -7\) where \(x\) is an integer.
• Therefore, Graph F is the correct representation.

Answer:

• (A) Continuous ray starting at -7 and pointing to the right
• (B) Continuous line covering all values
• (C) Continuous ray starting at -7 and pointing to the right with an open circle
• (D) Continuous ray starting at -7 and pointing to the left
• (E) Discrete points at -7, -8, -9, -10, ...
• (F) Discrete points at -7, -6, -5, -4, ... (Correct answer)