1. Equations
Courtesy of Les Edition CEC

2. Khan Academy: Equations Review
Evaluating Expressions in One Variable
Evaluating Expressions in 2 Variables
Evaluating Expressions with Variables Word Problems
Identifying Parts of Expressions
Why we do the same thing to both sides: Simple Equations
One Step Equation Intuition
Intuition Why We Divide Both Sides
Constructing and Solving Equations in the Real World 1
Find Out Missing Algebraic Step
Understanding the Process for Solving Linear Equations
Variables on Both Sides
Equations with Variables on Both Sides
Solving Equations in Terms of a Variable (advanced)

3. Equations
Numbers, symbols and operators (such as + and ×) grouped together that show the value of something.
Ex: 2x + 10 = 5

4. Equations vs. expressions
An equation says that two “things” are equal. These two “things” that we are comparing are mathematical expressions. An equal sign (=) is always used.
Ex: = 10 – 2

5. Equations vs Expressions
EQUATIONS (= sign)
Compares two expressions
EXPRESSIONS (no = sign)
4x - 8 = 4
3x2 - 2
x = 12x + 73
3a + 4b + 12
7 + 2 =
10 + 2x
4a + b = 8
3 + 2

6. Equivalent Equations
Equations are equivalent if they have the same solution(s)
2x = 14
5x = 3x + 14
5x - 8 = 3x + 6
All three of these equations are “equivalent equations” since x = 7 is the solution for each of them.

7. Equivalent equations
Proof:

8. Solving an Equation
The point is to get the variable alone (isolate) on one side of the equation.
The “equals” sign acts as the centre of a balance.
What you do on one side of the equation, you must do on the other side!
? + 3 = 10

9. Types of solutions There are three types of solutions for an equation.
One solution x = 7
No solution when the variable cancels out
2 = x - x ≠ 0
3) Infinite solutions x = x
GRAPH

10. Solving an equation BEDMAS (if there is anything to reduce).
Ex: 𝟑(𝟐𝒙+𝟔)=𝟐(𝟖 𝒙 −𝟒 )

11. Solving an equation
2) Put likes terms on one side of the equal sign. Do inverse operations! Reduce!
𝟔𝒙+𝟏𝟖=𝟏𝟔𝒙 −𝟖

12. Solving an equation
3) The x is attached to the -10 by a multiplication. You must do the equal and opposite of that, which means you divide by -10.
−𝟏𝟎𝒙=−𝟐𝟔

13. Solving Equations - Example 1
What you do on one side of the equation, you must do on the other side!

14. Solving Equations Proof

15. Solving Equations - Example 2
Continued on next slide

16. Solving Equations - Example 2

17. Solving Equations Proof

18. Constructing an Expression or an Equation
Word problems
Ex: The sum of Claude and Jean’s ages is 52 years. Jean is 10 years older than twice Claude’s age. Determine their ages.

19. Constructing an Expression or an Equation
Ex: The sum of Claude and Jean’s ages is 52 years. Jean is 10 years older than twice Claude’s age. Determine their ages.
Step 1: Determine the unknown(s)
The unknowns are:
Claude’s age
Jean’s age

20. Constructing an Expression or an Equation
Ex: The sum of Claude and Jean’s ages is 52 years. Jean is 10 years older than twice Claude’s age. Determine their ages.
Step 2: Represent each unknown with a variable or expression
Let: x represent Claude’s age
Jean’s age: x

21. Constructing an Expression or an Equation
Ex: The sum of Claude and Jean’s ages is 52 years. Jean is 10 years older than twice Claude’s age. Determine their ages.
Step 3: Construct an equation
Claude’s Age + Jean’s Age = 52
x + (10 + 2x) = 52

22. Solving Equations
Ex: The sum of Claude and Jean’s ages is 52 years. Jean is 10 years older than twice Claude’s age. Determine their ages.

23. Solving Equations
Ex: The sum of Claude and Jean’s ages is 52 years. Jean is 10 years older than twice Claude’s age. Determine their ages.
Since x = 14, we can now determine Jean’s age (PLUG 14 into x !!!)
Jean’s Age = x
= (14)
= 38