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Math 070 - Chapter 1
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Terms in this set (18)
Equation
A mathematical sentence that shows that two expressions are equivalent
Identities
Identities are equations that are true for all acceptable values of the variable.
Real Numbers
The set of all rational and irrational numbers
Rational Numbers
All positive and negative integers, fractions and decimal numbers.
Irrational Numbers
Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating.
Natural Numbers
The set of numbers 1, 2, 3, 4, ... Also called counting numbers.
Whole Numbers
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
Integers
The set of whole numbers and their opposites.
Irrational Numbers
Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating.
Contradictions
Equations in which the expression on the left side and the expression on the right side are never equal no matter what value is substituted for the variable.
Expression
A mathematical phrase that contains operations, numbers, and/or variables.
Conditional Equation
A conditional equation is true when using at least one replacement value for the variable and false when using at least one different replacement value for the variable for example X +6 equals 11 is only true if X is equal to 5X -7 equals -1 is only true if Y equals six.
Conditionally Equatiin with one variable is a linear equation
A conditional equation with one variable is a linear equation if the highest power of the variable is one to a power of one for example do you +5 equals 12 is a linear equation because the only variable that appears is being raised to the power of one T is equal to 2T to the first power however the equation I am to the second power plus 6M equals 16 is not a linear equation because it contains a variable that is being raised the power of two.
Equivalent equations
Two or more equations with the same solution
Addition property of equality
If you add the same number to each side of an equation, the two sides remain equal.
Subtraction property of equality
If you subtract the same number from each side of an equation, the two sides remain equal.
Division property of equality
If you divide each side of an equation by the same nonzero number, the two sides remain equal.
Multiplication property of equality
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