Download Solving Equations

Solving Equations
By: Marinda, Ashley, Trevor, and Ti’Shawn
Mrs. Sawyer
1st block
Essential Question
 Why is it important to be fair?
Unit Questions
 How do you justify the steps necessary to solve
equations?
 How does the understanding of balances and equality
relate to solving equations?
Content Questions
 How do you define a variable?
 What are the steps for solving equations?
1.02 Use formulas and algebraic expressions, including iterative and recursive
forms, to model and solve problems.
Student Objectives/Learning Outcomes
The learner will:
 properly use equality formulas to evaluate for the given variable
 solve equations using addition, subtraction, multiplication and
division
 solve two-step equations using addition, subtraction, multiplication
and division
 use the distributive property to combine like terms and solve
problems
 solve equations with variables on both sides
 identify equations as identity or no solution
 model distance-rate-time problems
 use a graphing calculator to check solutions of equations by
graphing
a=b
Addition Property of Equality
a+c=b+c
Substitution Property of
Equality
a–c=b–c
Multiplication Property of
Equality
a∙c=b∙c
Division Property of Equality
a = b
c c
Distributive Property
a(b + c) = ab + ac
a(b – c) = ab – ac
Addition Property of Equality
a+c=b+c
If 10 = 6 + 4,
then 10 + 2 = 6 + 4 + 2
Substitution Property of Equality
a–c=b–c
If 10 = 6 + 4,
then 10 – 2 = 6 + 4 – 2
Multiplication Property of Equality
a∙c=b∙c
If 2 ∙ 6 = 12,
then 2 ∙ 6 ∙ 5 = 12 ∙ 5
Division Property of Equality
a = b
c
c
If 5 + 1 = 6,
then 5 + 1 = 6
2
2
Distributive Property
a(b + c) = ab + ac
a(b – c) = ab – ac
If 3(4 + 1),
then 3(4) + 3(1)
Example: Solve each equation. Check your answer.
ONE STEP
a. x – 8 = 0
x–8+8=0+8
x=8
b. 4c = -96
4c = -96
4
4
c = -24
n/
=5
n/ (6) = 5(6)
6
n = 30
3/
6
4x
=9
(4/3)3/4x = 9(4/3)
x = 12