1.1 Linear Equations, Formulas, and Problem Solving Flashcards
What is an equation?
A statement that two expressions are equal.
Define a solution/root
Replacement values that make the equation true.
What are used to solve linear equations in one variable?
equivalent equations
What is an equivalent equation?
Those that have the same solution set.
What is the additive qualify of equality?
A = B if:
A + C = B + C
What is the multiplicative quality of equality?
A = B if:
AC = BC
or A/C = B/C
What are the steps for solving a linear equation in one variable?
1) eliminate parentheses using the distributive property , then combine any like terms.
2) Use the additive property of equality to write the equation with all variable terms on one side, and all constants on the other. Simplify.
3) Use the multiplicative property of equality to obtain an equation in the form of x = constant.
What do we do if the equation has fractional coefficients?
Multiply both sides by the least common denominator to make all coefficients whole numbers.
What is the type of equation that is true for some answers, but false for other?
Conditional equation.
What is the type of equation that is always true?
An identity.
What is a type of equation that is never true?
A contradiction.
What is a type of equation that has two or more variables?
A literal equation.
When we solve a literal equation for a given variable, x, what is the term for x?
The object variable.
