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Part III: All s Fair in Math and War: Arithmetic Skills
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Remember to include the sign, which indicates the answer is a positive or negative number Take the following simple quadratic equation: 7y2 = 28 1 First get rid of the pesky 7 by dividing both sides by 7 The result is y2 = 4 2 Using the square root rule, you then take the square root of both sides of the equation y2 = y and 4 = 2 y= 2 The above steps work with simple quadratic equations, but when you re solving a complex quadratic equation, you put all the terms on one side of the equal sign, making the equation equal zero In other words, get the quadratic equation into this form: ax2 + bx + c = 0, where a, b, and c are numbers and x is unknown Take a look at the following equation: x2 2x = 15 You can convert this equation to quadratic form by subtracting 15 from both sides of the equation x2 2x 15 = 0 The most efficient way to solve most quadratic equations is by factoring the equation and then setting each separate factor equal to zero See the section Factoring to find original numbers earlier in this chapter Look at this equation again: x2 2x 15 = 0 (x 5)(x + 3) = 0 x 5 = 0 and x + 3 = 0 x = 5 and x = 3 The solution for x2 2x 15 is 5, 3
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All math isn t created equal: Solving inequalities
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Some algebra problems state that two numbers aren t equal to each other (thus they re inequalities) In an inequality, the first number is either greater than ( ) or less than ( ) the second Just like with equations, the solution to an inequality is a value that makes the inequality true For the most part, you solve inequalities the same as you would solve a normal equation There are some facts of inequality life you need to keep in mind, however Short and sweet, here they are: Negative numbers are less than zero and less than positive numbers Zero is less than positive numbers but greater than negative numbers Positive numbers are greater than negative numbers and greater than zero
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8: Mathematics Knowledge
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A regular algebraic equation includes the equal sign (=), because the very basis of the equation is that one side of the equation must equal the other Quite the opposite is true with inequalities, and they have their own special symbols, used to express the differences: means does not equal in the way that 3 does not equal 4 or 3 4 > means greater than in the way that 4 is greater than 3 or 4 > 3 < means less than in the way the 3 is less than 4, or 3 < 4 means less than or equal to in the way that x may be less than or equal to 4 or x 4 means greater than or equal to in the way that x may be greater than or equal to 3 or x 3 To solve an inequality, you follow the same rules as you would for solving any other equation For example, check out this inequality: 3+x 4 To solve it, simply isolate x by subtracting 3 from both sides of the equation: 3+x 3 4 3 or x 1 The only exception to this rule is when you multiply or divide both sides of the inequality by a negative number In that case, the inequality sign is reversed So, if you multiply both sides of the inequality 3 < 4 by 4, your answer is 12 > 16
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