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Review of Must-Knows About Inequalities

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This document provides an overview of inequalities and how to solve them. It defines common inequality symbols such as >, <, , and and explains how to solve inequalities similarly to equations except when multiplying or dividing by a negative number. The document also discusses how to translate verbal expressions into mathematical inequalities and explains special solutions that result in all real numbers or no solution.

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Inequalities Review Preparing for your Post-Assessment
Symbols and Their Meanings Symbol Meaning(s) > Greater than, bigger than, more than, all numbers to the right of < Less than, smaller than, all numbers to the left of Greater than or equal to, at least, no less than, all numbers to the right and including Less than or equal to, at most, no more than, all numbers to the right and including
Solving inequalities is a lot like solving equations Except we have to switch our inequality symbol if we multiply or divide on both sides by a negative! Example: -2x < 4 requires me to divide by -2 on both sides to isolate x I would switch my symbol, and my answer would be x > -2
We also have to be able to translate verbal expressions into inequalities. I can spend no more than $100 at the mall. As an inequality, this could be 100, where x represents how much I can spend. I can spend at least $100 at the mall. As an inequality, this could be 100, where x represents how much I can spend.
Special Solutions When you are solving an inequality and the variable disappears: You get a true statement like 0 > -5 The solution to your inequality is all real numbers This happens because any value for your variable will create a true statement So, any number in the whole wide world would work for your variable! You get a false statement like 0 < -5 The solution to your inequality is no solution This happens because no value for your variable will create a true statement So, no number in the whole wide world would work for your variable

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Review of Must-Knows About Inequalities

  • 1. Inequalities Review Preparing for your Post-Assessment
  • 2. Symbols and Their Meanings Symbol Meaning(s) > Greater than, bigger than, more than, all numbers to the right of < Less than, smaller than, all numbers to the left of Greater than or equal to, at least, no less than, all numbers to the right and including Less than or equal to, at most, no more than, all numbers to the right and including
  • 3. Solving inequalities is a lot like solving equations Except we have to switch our inequality symbol if we multiply or divide on both sides by a negative! Example: -2x < 4 requires me to divide by -2 on both sides to isolate x I would switch my symbol, and my answer would be x > -2
  • 4. We also have to be able to translate verbal expressions into inequalities. I can spend no more than $100 at the mall. As an inequality, this could be 100, where x represents how much I can spend. I can spend at least $100 at the mall. As an inequality, this could be 100, where x represents how much I can spend.
  • 5. Special Solutions When you are solving an inequality and the variable disappears: You get a true statement like 0 > -5 The solution to your inequality is all real numbers This happens because any value for your variable will create a true statement So, any number in the whole wide world would work for your variable! You get a false statement like 0 < -5 The solution to your inequality is no solution This happens because no value for your variable will create a true statement So, no number in the whole wide world would work for your variable