1-8 An Introduction to Equations

VocabularyEquation: A mathematical sentence

that uses an equal sign.Open Sentence: An equation is an

open sentence if it contains one or more variables and it may be true or false depending on the value of the variables.

Solution of an equation: Any value or values that make an equation true.

Problem #1Classifying EquationsIs the equation true, false, or

open? Explain.If an equation contains only

numbers, simplify each side to determine if the expressions are equal. If there is a variable in the equation, it is open.

Problem #2Identifying Solutions of EquationsTo determine whether a number is

a solution to the equation, substitute the number for the variable in the equation. Simplify each side to determine whether the equation is true.

Problem #3Writing an EquationIn real-world problems, the word is

can indicate equality. You can represent some real-world problems using an equation.

Problem #4Using Mental Math to Find SolutionsUse mental math to find the

solution to the equation.

Ask yourself, “what number subtracted from 12 is 3?”

Problem #5Using a Table to Find a SolutionUse a table to find the solution to the

equation. Use mental math to substitute values like 0, 1, or 10. Use these values to find a good starting point for your table.

Problem #6Estimating a SolutionTo estimate a solution, find the

integer values of x between which the solution must lie. Use a table.