Problem 78 Rewrite each statement with \(&g... [FREE SOLUTION]

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Chapter 0: Problem 78

Rewrite each statement with $>$ so that it uses $<$ instead. Rewrite each statement with $<$ so that it uses $>. $$ -6<1 $$

Short Answer

Expert verified

1 > -6

Step by step solution

Understand the inequality

We need to rewrite the inequality \[-6 < 1\] using the greater than symbol (\[>\]).

Apply the inequality property

To convert an inequality from $<$ to $>$, reverse the direction of the inequality and switch the sides of the inequality. For \[-6 < 1\], switching sides, we get \[1 > -6\].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Reversing Inequality Signs

When dealing with inequalities, sometimes we need to flip the inequality sign. For instance, changing a less than sign (<) to a greater than sign (>). The key is to keep the inequality true by reversing the sense of the relation.

Consider the inequality $-6 < 1$. To reverse the sign, we switch both sides of the inequality. This means rewriting it as $1 > -6$.

This is crucial for solving many algebra problems because it allows you to manipulate the terms in a way that fits your needs while maintaining the true relationship between the values.

Inequality Properties

Inequalities share some useful properties that help us understand and manipulate them. Here are a few key properties:

If you add or subtract the same number from both sides, the direction of the inequality does not change. For instance, in $a < b$, adding $c$ to both sides yields $a + c < b + c$.
If you multiply or divide both sides of an inequality by a positive number, the direction of the inequality remains the same. For example, in $a < b$, multiplying both sides by a positive $c$ leads to $ac < bc$.
However, if you multiply or divide both sides by a negative number, you must reverse the inequality sign. For example, in $a < b$, if you multiply by a negative $c$, it becomes $ac > bc$.

These properties help keep inequalities true and allow for flexibility when solving algebra problems.

Symbol Transformation in Inequalities

Sometimes, transforming symbols in inequalities can be confusing. One of the most common transformations is switching between $>$ and $ <$.

Here's a simple rule: Whenever you need to change $a < b$ to a form with $>$, just switch the positions of $a$ and $b$. This gives you $b > a$.

Similarly, going from $ a > b$ to $ <$ involves swapping sides again to get $b < a$.

This transformation maintains the integrity of the inequality, making it a critical skill in algebra. Always double-check your work to ensure the transformation is accurate.

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91影视

Rewrite each statement with \(>\) so that it uses \(<\) instead. Rewrite each statement with \(<\) so that it uses $>. $$ -6<1 $$

Short Answer

Step by step solution

Understand the inequality

Apply the inequality property

Key Concepts

Reversing Inequality Signs

Inequality Properties

Symbol Transformation in Inequalities

One App. One Place for Learning.

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