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30 Cards in this Set

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  • Back
Equation
statement that two expressions are equal
Variables
letters that represent numbers
algebraic expression
form by numbers and variables connected by the operations of addition, subtraction, multiplication, division, raising to powers, and/or taking roots.
to evaluate an algebraic expression containing variables...
substitue the given numbers for the variables and simplify.
value of the expression
the result from evaluating an algebraic expression containing variables
natural numbers
1,2,3,4...
whole numbers
0,1,2,3...
intergers
...-3,-2,-1,0,1,2,3...
ellipsis
[...] it means the pattern continues
elements
members of a set
Set builder notation
describes the elements of a set but does not list them
real numbers [x]
x corresponds to a point on the number line
Rational numbers [a/b]
a and b are intergers and b does not equal 0
Irrational numbers [x]
x is a real number and x is not a rational number
3 is an element of set A. we write it like...
3EA
Subset
If all the elements of set A are also in set B ACB
IaI=
a if a is 0 or a positive number. -a if a is a negative number
The opposite of a number a
-a
A linear equation in one variable
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
Equivalent equations
have the same solution
addition property of equality
guarantees that the same number may be added to (or subtracted from) both sides of an equation, and the result is an equivalent equation
multiplication property of equality
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
to solve linear equations in one variable
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
exponent `
shorthand notation for repeated multiplication of the same factor
Formula
an equation that describes a know relationship among quantities is called a formula
to solve a formula for a specified variable
use the steps for solving an equation. Treat the specified variable as the only variable of the equation.
linear inequality in one variable
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.
addition property of inequality
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.
multiplication property of inequality
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
to solve a linear inequality in one variable
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