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1.7 – Solving Equations: An Introduction An equation is a mathematical sentence that uses an equal sign to state that two expressions represent the same number or are equivalent. (Example: 3 2 5 ) An equation that contains at least one variable is called an open sentence. (Example: x 5 12 ) The set of numbers from which you can select replacements for the variable is called the replacement set. A replacement for a variable that makes an equation true is called a solution. To solve an equation means to find all of its solutions. The collection of all the solutions is called the solution set. Example 1 – Solve 3x x 5 for 0,1,2 2 Two equations are equivalent if one can be obtained from the other by a sequence of the following steps: o You can: add the same number to both sides of an equation subtract the same number from both sides of an equation multiply both sides of an equation by the same nonzero number divide both sides of an equation by the same nonzero number Example 2 – Each pair of equations is equivalent. What was done to the first equation to get the second one? a. 3x 1 x 3x 2 x 1 b. L8 – pg 36 (5-9 odd & 19-23 all, 25 & 27) x5 7x 2x 5 27 x