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Algebra

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Inequalities

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The only difference between the linear equation "x + 3 = 2" and this linear inequality is that I have a "less than" sign, instead of an "equals" sign. The solution method is exactly the same: subtract 3 from either side. Note that the solution to a "less than, but not equal to" inequality is graphed with a parentheses (or else an open dot) at the endpoint, indicating that the endpoint is not included within the solution. Note that "x" in the solution does not "have" to be on the left. However, it is often easier to picture what the solution means with the variable on the left. Don't be afraid to rearrange things to suit your taste. 3) 4x + 6 >= 3x ? 5, then x <= ?11 -2x > 4, then x < -2 Graphically, the solution is: graphical solution

The Order of Operations

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Please Excuse My Dear Aunt Sally. ( Parenthesis, Exponents, Multiply, Divide, Add, Subtract )

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How to figure out hard math problems.

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Having trouble figuring out problems like 2+2? Its 4 :)

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Math review

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Math review Arithmetic sequence The notation of an arithmetic sequence is: where an is the nth term of the sequence and d is the difference between consecutive terms. In order to find the sum of the first n terms, simply find the value of the average term and then multiply that average by the number of terms you are summing. Geometric sequence Whereas in an arithmetic sequence the difference between consecutive terms is always constant, in a geometric sequence the quotient of consecutive terms is always constant. To find the nth term of a geometric sequence, use the following formula: To find the sum of the first n terms of a geometric sequence, use the following formula: where ?1 < r < 1. The Powers of i

how to solve logs

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1. To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable. Example 1: Solve for x in the equation Ln(x)=8. Solution: Step 1: Let both sides be exponents of the base e. The equation Ln(x)=8 can be rewritten . Step 2: By now you should know that when the base of the exponent and the base of the logarithm are the same, the left side can be written x. The equation can now be written . Step 3: The exact answer is and the approximate answer is Check: You can check your answer in two ways. You could graph the function Ln(x)-8 and see where it crosses the x-axis. If you are correct, the graph should cross the x-axis at the answer you derived algebraically.

solving exponential equations

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to solve exponential equations without logarithms, you need to have equations with comparable exponential expressions on either side of the "equals" sign, so you can compare the powers and solve. In other words, you have to have "(some base) to (some power) equals (the same base) to (some other power)", where you set the two powers equal to each other, and solve the resulting equation. For example: Solve 5x = 53. Since the bases ("5" in each case) are the same, then the only way the two expressions could be equal is for the powers also to be the same. That is: x = 3

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