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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1) Powers of 10 refer to numbers like 1, 10, 100, 1000 that are 10 multiplied by itself a certain number of times, represented by exponents.
2) To multiply a number by a power of 10, move the decimal point to the right by the number of places represented by the exponent. To divide, move the decimal point left by the same number of places.
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Inequalities ppt revised
Here are the steps to solve each inequality and graph the solution:
1) m + 14 < 4
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Graph: m < -10
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y < -6
Graph: y < -6
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k > -30
Graph: k > -30
4) 2x + 5 ≤ x + 1
-x -x
x + 5 ≤ 1
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x ≤ -4
Graph: x ≤ -4
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This document discusses two types of geometric symmetry: line symmetry and rotational symmetry. It defines line symmetry as when a figure can be divided into two mirror image parts by a line, called the line of symmetry. Rotational symmetry occurs when a figure looks the same after being rotated partway around a center point. Regular polygons have both types of symmetry: their number of lines of symmetry equals their number of sides, and their rotational symmetry angle is 360 degrees divided by the number of sides. The document provides examples and exercises to help understand and identify these symmetries.
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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 𝑥 ≤ 100, where x represents how much I can spend. I can spend at least $100 at the mall. As an inequality, this could be 𝑥 ≥ 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