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

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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 \(| -3 | = 3\).

Rewrite the inequality by substituting the absolute value with its evaluated result: \(- | -3 | \geq -3\) becomes \(-3 \geq -3\).

Analyze the inequality \(-3 \geq -3\). This means "-3 is greater than or equal to -3."

Since the two sides are equal, the inequality holds true because the "equal to" part of "greater than or equal to" is satisfied.

Therefore, the statement is true.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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