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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)
x5

7x
2x  5  27  x 