Simplify each inequality if needed. Then determine whether the statement is true or false. 0 ≤ -5

검증된 단계별 안내

First, understand the inequality given: \(0 \leq -5\) means "0 is less than or equal to -5."

Recall the number line order: numbers increase as you move to the right. Zero is to the right of -5, so 0 is greater than -5.

Since 0 is greater than -5, the statement \(0 \leq -5\) is not true.

Therefore, the inequality cannot be simplified further because it is already in its simplest form.

Conclude that the statement \(0 \leq -5\) is false.

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주요 개념

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Understanding Inequalities

Inequalities compare two values or expressions, indicating if one is less than, greater than, or equal to the other. They can be simplified or manipulated similarly to equations, but special care is needed when multiplying or dividing by negative numbers, as this reverses the inequality sign.

Evaluating Inequality Statements

To determine if an inequality is true or false, substitute or analyze the values on both sides. For example, checking if 0 ≤ -5 involves comparing zero and negative five directly, understanding their positions on the number line.

Number Line and Order of Real Numbers

The number line visually represents real numbers in increasing order from left to right. Knowing that zero is greater than any negative number helps quickly assess inequalities like 0 ≤ -5, since zero lies to the right of -5, making the statement false.