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Algebra 2
1.3 Solving Linear Equations
Define
Equation
Linear Equation
Equivalent
Transformations that Produce Equivalent Equations
Addition Property of Equality
Add the same number to both sides
If a = b, then a + c = b + c
Subtraction Property of Equality
Subtract the same number from both
sides. If a = b then a – c = b – c
Multiplication Property of Equality
Multiply both sides by the same
number. If a = b, then ac = bc
Division Property of Equality
Divide both sides by the same
number. If a = b, then a/c = b/c
Variable on One Side
Ex. 4x – 7 = 21
3/7x + 9 = 15
Variable on Both Sides
Ex. 5n + 11 = 7n -9
Using the Distributive Property
Ex. 4(3x – 5) = -2(-x + 8) – 6x
Solving an equation with Fractions
1
1
1
x  x
4
6
Ex. 3

-3x + 7 = 8 + 5x