SAMPLE College Math

‭calculate‬ ‭the‬ ‭absolute‬ ‭value‬ ‭of‬ ‭-5,‬ ‭then‬ ‭it‬ ‭will‬ ‭be‬ ‭denoted‬ ‭by‬ ‭|-5|and‬ ‭is‬ ‭equal‬ ‭to‬ ‭5,‬ ‭showing‬ ‭that‬ ‭the‬ ‭distance from -5 to 0 is 5 units. Some of the properties of absolute values are:‬ | ‭ ‬| = {‭ ‬ ‭ ‬‭ ‬‭≥0‬ − ‭ ‬ ( )‭‬‭ ‬‭‬‭ ‬ < ‭0‬ || −‭ ‬ |‭ ‭≥‬‭ ‬| 0=‬ ‭ ‬| ‭ ‬‭ ‬‭ ‬| | ‭ ‬ * ‭ ‬| = ‭‬|‭‬‭ ‬‭‬| * |‭‬‭ ‬‭‬| ‭Scientific Notation‬ ‭Sometimes‬‭we‬‭make‬‭use‬‭of‬‭some‬‭power‬‭of‬‭10‬‭that‬‭makes‬‭it‬‭convenient‬‭to‬‭write‬‭a‬‭very‬‭large‬‭number;‬‭this‬ ‭means‬ ‭we‬ ‭are‬ ‭making‬ ‭use‬ ‭of‬ ‭scientific‬ ‭notation.‬ ‭For‬ ‭instance,‬ ‭suppose‬ ‭we‬ ‭have‬ ‭to‬ ‭write‬ ‭the‬ ‭number‬ ‭687657.788. We can write it as‬ ‭.‬ ‭6‬. ‭87657788×‬‭10‬ ‭5‬ ‭B. Inequalities‬ ‭The‬ ‭value‬ ‭of‬ ‭different‬ ‭numbers‬ ‭can‬ ‭be‬ ‭compared‬ ‭by‬ ‭their‬ ‭relative‬ ‭position‬ ‭on‬ ‭the‬ ‭number‬ ‭line.‬ ‭For‬ ‭instance, in the given number line below,‬

‭ ‬ ‭ ‬

‭ ‬‭‬ < ‭‬‭ ‬

‭ ‬

‭ ‬

‭is‬‭less‬‭than‬ ‭and‬‭is‬‭denoted‬‭by‬ ‭also‬ ‭say‬ ‭,‬ ‭that‬ ‭is‬ ‭is‬‭greater‬‭than‬ ‭and‬‭lies‬‭on‬‭the‬‭right‬‭side‬‭of‬‭the‬‭number‬‭line,‬‭relative‬‭to‬‭the‬ ‭ ‬‭‬ > ‭‬‭ ‬ ‭ ‬ ‭ ‬ ‭position of‬ ‭.‬ ‭ ‬ ‭The mathematical representation for different expressions is given in the following table:‬ ‭,‬‭which‬‭means‬ ‭lies‬‭to‬‭the‬‭left‬‭of‬ ‭on‬‭the‬‭number‬‭line.‬‭We‬‭can‬

‭ ‬ = ‭‬‭ ‬ ‭ ‬ < ‭‬‭ ‬ ‭ ‬ > ‭‬‭ ‬ ‭ ‬‭≥‬‭ ‬ ‭ ‬‭≤‬‭ ‬ ‭ ‬‭≠‬‭ ‬ ‭ ‬‭≈‬‭ ‬

‭Interpretations‬ ‭is equal to‬ ‭ ‬ ‭ ‬ ‭is less than‬ ‭ ‬ ‭ ‬ ‭is greater than‬ ‭ ‬ ‭ ‬ ‭is greater than or equal to‬ ‭ ‬ ‭ ‬ ‭is less than or equal to‬ ‭ ‬ ‭ ‬ ‭is not equal to‬ ‭ ‬ ‭ ‬

‭Expressions‬

‭is approximately equal to‬ ‭ ‬ ‭ ‬ ‭The‬ ‭symbols‬ ‭<,‬ ‭>,‬ ‭≥,‬‭≤‬‭and‬‭≠‬‭denote‬‭the‬‭signs‬‭of‬‭inequalities‬‭and‬‭the‬‭expressions‬‭using‬‭these‬‭signs‬‭of‬ ‭inequalities,‬ ‭,‬ ‭,‬ ‭,‬ ‭and‬ ‭denotes‬ ‭inequalities.‬ ‭We‬ ‭can‬ ‭make‬ ‭use‬ ‭of‬ ‭set-builder‬ ‭ ‬ < ‭ ‬ ‭ ‬ > ‭ ‬ ‭ ‬‭≥‬‭ ‬ ‭ ‬‭≤‬‭ ‬ ‭ ‬‭≠‬‭ ‬ ‭notation‬‭for‬‭these‬‭inequalities‬‭as‬‭well.‬‭For‬‭instance,‬ ‭means‬‭set‬ ‭represents‬‭all‬‭the‬‭values‬ ‭ ‬‭‬ = ‭‬{‭ ‬‭|‬‭‬‭ ‬‭≥‬‭‬‭2‬} ‭ ‬ ‭of‬ ‭such‬ ‭that‬ ‭is‬ ‭greater‬ ‭than‬ ‭or‬ ‭equal‬ ‭to‬ ‭2.‬ ‭This‬ ‭can‬ ‭be‬ ‭shown‬ ‭graphically‬ ‭on‬ ‭the‬ ‭number‬ ‭line‬ ‭as‬ ‭ ‬ ‭ ‬ ‭follows:‬

‭© 2023 ACHIEVE ULTIMATE CREDIT-BY-EXAM GUIDE‬‭|‬‭COLLEGE MATH‬

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