Simplify each inequality if needed. Then determine whether the statement is true or false. -|-3| ≥ -3

Verified step by step guidance

1. First, evaluate the absolute value expression inside the inequality. Recall that the absolute value of a number is its distance from zero on the number line, so \(| -3 | = 3\).
2. Rewrite the inequality by substituting the absolute value with its evaluated result: \(- | -3 | \geq -3\) becomes \(-3 \geq -3\).
3. Analyze the inequality \(-3 \geq -3\). This means "-3 is greater than or equal to -3."
4. Since the two sides are equal, the inequality holds true because the "equal to" part of "greater than or equal to" is satisfied.
5. Therefore, the statement is true.

Key Concepts

Absolute Value

The absolute value of a number represents its distance from zero on the number line, always yielding a non-negative result. For example, |−3| equals 3 because −3 is three units away from zero.

Inequality Symbols and Their Meaning

Inequalities compare two expressions using symbols like ≥ (greater than or equal to). Understanding these symbols helps determine if a statement like |−3| ≥ −3 is true by comparing the values correctly.

Properties of Absolute Value in Inequalities

Since absolute values are always non-negative, they are always greater than or equal to any negative number. This property simplifies inequalities involving absolute values and negative numbers.