2.3 Solving Multi-Step Equations:
Combining like Terms: Simplify the terms with the same variable using arithmetic.
Term: A number, a variable or a product or quotient of numbers and variables that is added or subtracted in an algebraic expression.
GOAL:
We solve multi-step equations by forming a series of simpler equations by first using combination of like terms:Ex: What is the solution of 5 = 5m – 23 + 2m5 = 5m – 23 + 2m5 = 5m + 2m – 23 5 = 7m – 23 Add like terms
+23 + 23 Inverse of subtraction28 = 7m __ ___
7 7Inverse of multiplication
m = 4 Don’t forget to check!!
Same variable
REAL-WORLD:
A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket for $19 per ticket. The web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy?
SOLUTION: Using the given info we have:
Each ticket (x) costs $167 167x
One time charge of $16 +16
The family paid = $1132
Insurance for each ticket is $19 19x
167x + 19x + 16 = 1132
167x + 19x + 16 = 1132
186x + 16 = 1132 Like terms
186x + 16-16 = 1132-16 Inverse of Add
186x = 1116 Like terms
186x /186 = 1116 /186 Inverse of mult.
x = 6 Tickets
YOU TRY IT:
What is the solution of
11x – 8 – 6x = 22
Solution:11x – 8 – 6x = 2211x – 6x – 8 = 22
5x – 8 = 22 Add like terms+ 8 = +8 Inverse of subtraction 5x = 30 __ ___
5 5Inverse of multiplication
x = 6 Don’t forget to check!!
Same variableGiven
Solving equations with Distributive Property:
Ex: What is the solution of – 8 (2x -1)= 36– 8 (2x -1)= 36– 8(2x) – 8(-1)= 36– 16x + 8 = 36 Multiplication
– 8 – 8 Inverse of addition _____ ____ – 16 – 16
Inverse of multiplication
x = - 28/16 - 7/4 Don’t forget to check!!
Distributive – 8
– 16x = 28
YOU TRY IT:What is the solution of
18 = 3(2x – 6 )?
Solution:18 = 3(2x – 6)18 = 3(2x) + 3(-6)
Multiplication +18 +18 Inverse of subtraction
__ ___ 6 6
Inverse of multiplication
x = 6 Don’t forget to check!!
Distributive 3
36 = 6x
18 = 6x – 18
Given
Solving equations with fractions:
Ex: What is the solution of - = 10?
Multiplication
Same Denominator
Common Denominator - = 10
- = 10
= 10
= 10 Subtraction
Inverse of Multiplication
12 = 10 12 Inverse of division
5 = 120
5 = 120 ___ ___ 5 5 = 24 Don’t forget to check!!
Check: - = 10 3(6) - 8 18 - 8 10 = 10
YOU TRY IT:
What is the solution of
+ = 3?
Solution:
Add the numerators
Common Denominator + = 3
+ = 3
= 3
= 3 Opposite of dividing by 20
Solution:
(20) = 3(20)
23b = 60 Opposite of multiplying by 23
b = Don’t forget to Check!
Multiply by 20 both sides
Check: + = 3
We never divide fractions,We keep, change and flip!
Plug in our answer + = 3
+ = 3
= 3
b =
) +
) + 24
+
45 Cross Cancel: Divide a numerator with a denominator (only on the same fraction)
𝟐𝟒+𝟒𝟓𝟐𝟑 = 3
Add the numerators: since our denominators are the same.
𝟔𝟗𝟐𝟑 = 3
Since 69/23 = 3 and 3 =3 we have gotten the right answer.
VIDEOS: Multi-Step Equations
Multi-Stephttp://www.khanacademy.org/math/algebra/rational-expressions/solving-rational-equations/v/ex-1-multi-step-equationhttp://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/complicated_equations/v/ex-2-multi-step-equation
Class Work:
Pages: 97-100
Problems: As many as you need to master
the concepts.
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