Rewrite each statement with \u003e so that it uses . -5 \u003e -100

Understand that the inequality symbol can be reversed by swapping the sides of the inequality. For example, if you have $$a \u003e b$$, you can rewrite it as $$b -100. $$This means that $$-5 is $$greater than $$-100. To $$rewrite this inequality using the symbol $$ -100 is $$equivalent to $$-100 \u003c -5$$ when rewritten with the $$\u003c$$ symbol.

Ch. R - Algebra Review

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Lial 12th Edition

Ch. R - Algebra Review

문제 79

1장, 문제 79

Rewrite each statement with > so that it uses < instead. Rewrite each statement with < so that it uses >. -5 > -100

검증된 단계별 안내

Understand that the inequality symbol can be reversed by swapping the sides of the inequality. For example, if you have $a > b$, you can rewrite it as $b < a$.

Look at the given inequality: $-5 > -100$. This means that $-5$ is greater than $-100$.

To rewrite this inequality using the symbol $<$, swap the two sides and change the symbol accordingly: $-100 < -5$.

Check the rewritten inequality to ensure it makes sense on the number line: since $-100$ is less than $-5$, the inequality $-100 < -5$ is correct.

Thus, the original inequality $-5 > -100$ is equivalent to $-100 < -5$ when rewritten with the $<$ symbol.

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주요 개념

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Inequality Symbols and Their Meaning

Inequality symbols like > (greater than) and < (less than) compare two values, indicating which is larger or smaller. Understanding these symbols is essential to correctly interpret and rewrite inequalities by reversing the direction of comparison.

Reversing Inequalities

When rewriting inequalities, changing a 'greater than' (>) to a 'less than' (<) symbol involves flipping the inequality sign while keeping the values in the same order. This concept helps in expressing the same relationship from a different perspective.

Number Line and Negative Numbers

Understanding the position of negative numbers on the number line is crucial, as it affects the truth of inequalities. For example, -5 is greater than -100 because it lies to the right on the number line, which helps in correctly rewriting inequalities involving negatives.