1.1 Linear, Rational and Absolute Value Equations Flashcards
a statement (or sentence) indicating that two algebraic expressions are equal
equation
values for the variable of an equation that make an equation true
solution or root
an equation that has yet to be determined whether the values of the variable are true or false. An equation is neither true or false until we choose a value of x.
open sentence
the set of all solutions to an equation
solution set
symbols for solution set
{ }
two or more equations with the same solution set
equivalent equations
an equation of the form ax + b = 0, where a and b are real numbers with a not equal to 0.
Linear equation in one variable
an equation that is satisfied by every real number for which both sides are defined (infinitely many solutions)
identity
an equation that satisfied by at least one real number but is not an identity
conditional equation
an equation that has no solution
inconsistent equation
a root that did not satisfy the original equation because the domain of the rational expression excluded the root.
extraneous root
a set with no members or an equation that has no solution
empty set
symbol used to represent the empty set
How do you solve an equation that has fractions with variables in the denominator?
1) State the restrictions within the domain.
2) Find an LCD and use it to remove the fractions entirely.
3) Solve the equation normally.
4) Check that the solutions are not also restrictions. If so, these are extraneous and cannot be solutions.
What are the steps to solve an absolute value equation?
1) Isolate the absolute value.
2) Write two equations removing the absolute values and changing the signs to one of the equations on the opposite side of the absolute value and keeping the sign for the other equation.
3) Solve both equations.
4) Check the solutions
