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30 Cards in this Set
- Front
- Back
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Equation
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statement that two expressions are equal
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Variables
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letters that represent numbers
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algebraic expression
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form by numbers and variables connected by the operations of addition, subtraction, multiplication, division, raising to powers, and/or taking roots.
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to evaluate an algebraic expression containing variables...
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substitue the given numbers for the variables and simplify.
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value of the expression
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the result from evaluating an algebraic expression containing variables
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natural numbers
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1,2,3,4...
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whole numbers
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0,1,2,3...
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intergers
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...-3,-2,-1,0,1,2,3...
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ellipsis
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[...] it means the pattern continues
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elements
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members of a set
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Set builder notation
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describes the elements of a set but does not list them
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real numbers [x]
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x corresponds to a point on the number line
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Rational numbers [a/b]
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a and b are intergers and b does not equal 0
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Irrational numbers [x]
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x is a real number and x is not a rational number
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3 is an element of set A. we write it like...
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3EA
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Subset
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If all the elements of set A are also in set B ACB
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IaI=
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a if a is 0 or a positive number. -a if a is a negative number
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The opposite of a number a
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-a
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A linear equation in one variable
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an equation that can be written in the form ax + b = c, where a,b, and c are real numbers and a is not 0
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Equivalent equations
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have the same solution
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addition property of equality
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guarantees that the same number may be added to (or subtracted from) both sides of an equation, and the result is an equivalent equation
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multiplication property of equality
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guarantees that both sides of an equaiton may be multiplied by (or divided by) the same nonzero number, and the result is an equivalent equation
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to solve linear equations in one variable
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1. clear the equation of fractions 2. remove grouping symbols such as parentheses 3. simplify by combing like terms 4.write variable terms on one side and nubmers on the other side using the same property of equality 5. isolate the variable using the muliplication property of equality 6. check the proposed solution in the original equation
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exponent `
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shorthand notation for repeated multiplication of the same factor
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Formula
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an equation that describes a know relationship among quantities is called a formula
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to solve a formula for a specified variable
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use the steps for solving an equation. Treat the specified variable as the only variable of the equation.
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linear inequality in one variable
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an inequality that can be written in the form ax + b < c, where a, b, and c are real numbers and a does not equal 0.
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addition property of inequality
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guarantees that the same number may be added to (or subtracted from) both sides of inequality, and the resulting inequality will have the same solution set.
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multiplication property of inequality
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guarantees that both sides of an inequality may be multiplied by (lr dived by) the same positive number and the resulting inequality will have the same solution set. We may also multiply (or divide) both sides of an inquality of the same negative number and reverse the direction of the inequality symbol
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to solve a linear inequality in one variable
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1. clear the equation of fractions 2. remove grouping symbols such as parentheses 3. simplify by combining like terms 4. write variable terms on one side and numbers on the other side using the addition property of inequality 5. Isolate the variable using the muliplication property of inequality
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