Question

1. which graph represents the solution to \\(|x| < 6\\)?

no solution

Explanation:

Interpret the absolute value inequality

Using the Absolute Value Inequalities knowledge point

$$ |x| < 6 \iff -6 < x < 6 $$

Identify the graphical representation

Using the Graphing Inequalities knowledge point

• The solution set is the open interval \((-6, 6)\).
• On a number line, this is represented by open circles at \(-6\) and \(6\) with a shaded line segment connecting them.
• Looking at the options:
• Option 1: "no solution"
• Option 2: Shaded line covering all numbers from \(-5\) to \(5\) (and beyond) with arrows on both ends.
• Option 3: Open circles at \(-6\) and \(6\) with shading pointing outwards to the left and right.
• Option 4: Open circles at \(-6\) and \(6\) with shading between them.
• Therefore, the fourth option is the correct graph.

Answer:

• (A) no solution
• (B) a number line shaded entirely with arrows on both ends
• (C) a number line with open circles at -6 and 6, shaded outwards to the left and right
• (D) a number line with open circles at -6 and 6, shaded between them (Correct answer)