Determine whether each statement is true or false. -13 ≤ -2

Verified step by step guidance

1. Identify the inequality given: \(-13 \leq -2\).
2. Recall that the symbol \(\leq\) means "less than or equal to." So the statement says "-13 is less than or equal to -2."
3. Compare the two numbers on the number line: -13 is to the left of -2, which means -13 is indeed less than -2.
4. Since -13 is less than -2, the inequality \(-13 \leq -2\) is true.
5. Therefore, the statement is true because the inequality holds as written.

Key Concepts

Inequality Symbols and Their Meaning

Inequality symbols like ≤ (less than or equal to) compare two values to show their relative size. The symbol ≤ means the value on the left is either less than or exactly equal to the value on the right.

Number Line and Ordering of Integers

Integers are ordered on a number line from left (smaller) to right (larger). Understanding that -13 is to the left of -2 helps determine that -13 is less than -2, which is essential for evaluating inequalities.

Evaluating True or False Statements in Inequalities

To determine if an inequality is true or false, substitute the values and check if the relationship holds. For example, check if -13 ≤ -2 by comparing their positions on the number line or their numeric values.