Students are introduced to the formal process of solving an equation: starting from the assumption that the original equation has a solution. Students explain each step as following from the properties of equality.
Students identify equations that have the same solution set.
Lesson 12 Summary
If is a solution to an equation, it will also be a solution to the new equation formed when the same number is added to (or subtracted from) each side of the original equation, or when the two sides of the original equation are multiplied by (or divided by) the same non-zero number. These are referred to as the Properties of Equality.
If one is faced with the task of solving an equation, that is, finding the solution set of the equation:
Use the commutative, associative, distributive properties, AND use the properties of equality (adding, subtracting, multiplying by non-zeros, dividing by non-zeros) to keep rewriting the equation into one whose solution set you easily recognize. (We believe that the solution set will not change under these operations.)
Determine which of the following equations have the same solution set by recognizing properties, rather than solving.
a. 2x + 3 = 13 - 5x
b. 6 + 4x = -10x + 26
c. 6x + 9 = 13/5 - x
d. 0.6 + 0.4x = -x + 2.6
e. 3(2x + 3) = 13/5 - x
f. 4x = -10x + 20
g. 15(2x + 3) = 13 - 5x
h. 15(2x + 3) + 97 = 110 - 5x
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