Rewrite each statement with \u003e so that it uses . -9 \u003c 4

Ch. R - Algebra Review

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Lial 12th Edition

Ch. R - Algebra Review

문제 77

1장, 문제 77

Rewrite each statement with > so that it uses < instead. Rewrite each statement with < so that it uses >. -9 < 4

검증된 단계별 안내

Identify the inequality symbol in the given statement. Here, the statement is \(-9 < 4\), which uses the less than symbol \(<\).

Recall that the inequality \(a < b\) means that \(a\) is less than \(b\). To rewrite this using the greater than symbol \(>\), we reverse the inequality and swap the two sides.

Swap the two sides of the inequality: the left side becomes \(4\) and the right side becomes \(-9\).

Change the inequality symbol from \(<\) to \(>\) to maintain the truth of the statement after swapping.

Write the new inequality as \(4 > -9\), which is the equivalent statement using the greater than symbol.

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주요 개념

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Inequality Symbols and Their Meaning

Inequality symbols like < (less than) and > (greater than) compare two values to show their relative size. Understanding what each symbol represents is essential to correctly interpret and rewrite inequalities.

Reversing Inequalities

When rewriting inequalities by switching the direction of the symbol, the inequality sign must be reversed. For example, if the original statement is a < b, rewriting it with > requires changing it to b > a.

Properties of Inequalities with Negative Numbers

Working with negative numbers in inequalities requires careful attention, as their order on the number line is reversed compared to positive numbers. Recognizing how negative values relate helps avoid mistakes when rewriting inequalities.