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11 Cards in this Set
- Front
- Back
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variable
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unknown quantity; Letters such as x or n are used to represent unknown quantities. For example, suppose Pam has 5 more pencils than Fred has. If F represents the number of pencils that Fred has, then the number of pencils that Pam has is F + 5. As another example, if Jim’s present salary S is increased by 7%, his new salary is 1.07 S.
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algebraic expression
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consists of terms
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coefficient
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19 in 19x
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constant term
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3 (no power)
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second degree (or quadratic) polynomial in x
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highest power of x is 2; The expression F + 5 is a first degree (or linear) polynomial in F since the highest power of F is 1.
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Manipulating Algebraic Expressions
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When working with algebraic expressions, it is often necessary to factor them or combine like terms. For example, the expression 6x + 5x is equivalent to (6 + 5)x, or 11x. In the expression 9x - 3y, 3 is a factor common to both terms: 9x - 3y = 3(3x - y).
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Solving Linear Equations with One Unknown
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To solve a linear equation with one unknown (that is, to find the value of the unknown that satisfies the equation), the unknown should be isolated on one side of the equation. This can be done by performing the same mathematical operations on both sides of the equation.
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Solving Equations by Factoring
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To do this, first add or subtract expressions to bring all the expressions to one side of the equation, with 0 on the other side. Then try to factor the nonzero side into a product of expressions. If this is possible, then each of the factors can be set equal to 0, yielding several simpler equations that possibly can be solved. The solutions of the simpler equations will be solutions of the factored equation. The solutions of an equation are also called the roots of the equation. These roots can be checked by substituting them into the original equation to determine whether they satisfy the equation.
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Exponents
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A positive integer exponent of a number or variable indicates a product, and the positive integer is the number of times that the number or variable is a factor in the product.
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inequalities
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An inequality is a statement that uses one of the following symbols: not equal to, > greater than, greater than or equal to, < less than, less than or equal to
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function
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An algebraic expression in one variable can be used to define a function of that variable. A function is denoted by a letter such as f or g along with the variable in the expression.
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