Upload
aron-oneal
View
218
Download
2
Tags:
Embed Size (px)
Citation preview
2.1 Solving One Step Equations:
Equivalent Equations: equations that have the same solutions.
Isolate: Get a variable with a coefficient of 1 alone on one side of the equation.
Inverse Operations: Opposite operations that undo other operations.
GOAL:
We can find the solution to one step equations by using inverse operations:
Addition Property: for any real numbers a, b, and c,
if a = b, then a + c = b + c
Ex: Solve x – 3 = 2
Notice that we use the inverse of subtraction which Is addition to isolate the variable x.
+ 3 + 3 x = 5
Check: ( ) - 3 = 2 (5)- 3 = 2
2 = 2
We can find the solution to one step equations by using inverse operations:
Subtraction Property: for any real numbers a, b, and c,
if a = b, then a - c = b - c
Ex: Solve x + 3 = 2
Notice that we use the inverse of addition which Is subtraction to isolate the variable x.
- 3 - 3 x = - 1
Check: ( ) + 3 = 2 (-1)+ 3 = 2
2 = 2
We can use this procedure no matter where the variable is places, left or right of the equal sign:
Ex: Solve ½ = y – 3/2 + 3/2 + 3/2
4/2 = y
Check: ½ = ( ) – 3/2 ½ = ( 2) – 3/2 ½ = (4/2) – 3/2
½ = ½
2 = y
Remember that when you add or subtract fractions we must find a common denominator!!
Multiplication Property: for any real numbers a, b, and c,
if a = b, then a c∙ = b c∙
Ex: Solve = 12
Notice that we use the inverse of division which Is multiplication to isolate the variable m.
m = 84
Check: = 12 = 12
= 12 12 = 12
(7) = 12(7)
Division Property: for any real numbers a, b, and c,
if a = b, then =
Ex: Solve 4z= 12
Notice that we use the inverse of multiplication which is division to isolate the variable m.
z = 3
Check: 4z = 12 4( ) = 12 4(3) = 12 12 = 12
__ __ 4 4
Solve:
Thus: 36 = t
The fraction is multiplying t thus the opposite is division. However, we never divide fractions. We always use the inverse of the given fraction.
36 = t
= t t =
Don’t forget to check your answer!!!
Check:
Thus we have the correct answer.
YOU TRY IT:
What is the solution to
SOLUTION:
inverse of division
x=−𝟑𝟔
VIDEOS: One StepEquations
One Step:
http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/e/one_step_equations
Class Work:
Pages: 85 – 87
Problems: As many as you need to master
the concepts.