Solving linear equations

1. Algebra
Solving Linear Equations

2. • Solve linear equations with an unknown on both sides.
• Solve linear equations with fractions and an unknown on both sides.
• Solve linear equations with brackets and an unknown on both sides.
To solve more complicated linear equations.
Learning Objective
Success Criteria

3. How much can you say?
On your mini white board, write down
anything you can about this equation.
You have 2 minutes!
Starter: Snowballs
3 + 2 x 4
20 ÷ 4 + 3
2
Star
t
Stop

4. Reflection
3 + 2 x 4 = 11
20 ÷ 4 + 3 8
2 14

5. Let’s think together:
I have a bag of marbles and 5 extras. Altogether I have
13 marbles. How many marbles are in the bag?
+ = 13

6. m + = 13
+ = 13
Can I say ?

7. says that two expressions are
equal. Equations can have
unknown values, usually shown as
letters.
An equation

8. These are examples of equations:
3 5 = 10 + 5
5 + a = 20
5b = 20
5c + 5 = 20
20 5
− p = 7 + q
Unknown values are represented by letters.
Both sides of
the equation
are equal

9. Guided Practice
Example 1:
Solve 4a = 26
1)Locate the unknown
a

10. 2)Clean up by inverse operations
Solve 4a = 26
÷ 4
a

11. 3)Keep the balance
Solve 4a = 26
÷ 4 ÷ 4
a = 6.5

12. 4)Check your answer
Solve 4a = 26
4(6.5)=26√

13. Guided Practice
Example 2:
Solve 5a 12 = 18
−
1)Locate the unknown
a

14. 2)Clean up by inverse operations
Solve 5a 12 = 18
−
+ 12
5a

15. 3)Keep the balance
Solve 5a 12 = 18
−
+ 12
+ 12
5a = 30

16. 5a = 30
2)Clean up by inverse operations
÷ 5
a

17. 3)Keep the balance
5a = 30
÷ 5 ÷ 5
a = 6

18. 4)Check your answer
5(6) 12 =18
− √
Solve 5a 12 = 18
−

19. Guided Practice
Example 3:
Solve 8y + 5 = 101
1)Locate the unknown
2)Clean up by inverse operations
3)Keep the balance
4)Check your answer
− 5 − 5
8y = 96
÷ 8 ÷ 8
y = 12
Check your answer
Solve 8y + 5 = 101
8(12) + 5 = 101√

20. Solve
Guided Practice
Example 4:
1)Locate the unknown
2)Clean up by inverse operations
3)Keep the balance
4)Check your answer
Clue
To rearrange the
equation with this
division, you need to
multiply both sides by y.
X X
30y = 11
y =
÷ 30 ÷ 30

21. Guided Practice
Example 5:
Solve
1)Locate the unknown
2)Clean up by inverse operations
3)Keep the balance
4)Check your answer
− 6
− 6
X
X
7y = 49
÷ 7 ÷ 7
y = 7
Check your answer
Solve
7 + 6
13 √

22. Guided Practice
Example 6:
Solve 12 - a = 18
−12 −12
-a = 6
÷(−1) ÷(−1)
a = -6
Check your answer
Solve 12 - a = 18
Solve 12 – (-6)= 18
√

23. FUN TIME
Adventures Cards

24. Some equations have unknowns on
both sides of the equation:
8x + 4 = 20 2
− x
Do you know that:

25. A bar model is another useful way to represent
an equation.
The diagram can help you see how to calculate the
solution.
x x
20
16
x
2x + 16 = x + 20

26. Write down an equation to match
the balance problem
Explore
+ + + 7 = 25 +
3 + 7 = 25 +

27. Guided Practice
Example 7:
5a + 5 = 3a + 17
5a - 3a =17 - 5
2a = 12
a = 6
a = 6
First
Combine
like terms
and take
care of
signs
÷ 2 ÷ 2

28. Guided Practice
Example 8:
Write expressions, in simplest form, for the perimeters of
the parallelogram and hexagon below

29. Perimeter of
parallelogram =2+3+2
+3 +3 +3 + 2
Perimeter of
Hexagon =+7)+ +4)
+14 + + 16
= + + 14 + 16
= +30

30. Guided Practice
Example 9:
I think of a number, n. I divide it by 3 and add 7.
This gives the same answer as when I divide the number by
2. Write an equation in n and solve it to find the number I
thought of
1)Combine like terms and take care of signs
2)Locate the unknown
3)Clean up by inverse operations
4)Keep the balance
5)Check your answer

31. = -7
= -7
= -7
- = -7
÷ −
𝟏
𝟔
÷ −
𝟏
𝟔
n = -7
n= -7
-7
n= 42
𝒏
𝟑
+𝟕=
𝒏
𝟐

32. Guided Practice
Example 10:
Solve the equation:
Clue
Expand the brackets
or divide. Choose
which is easier
Expand the brackets
5(2 x + 6) = 90
10 x + 30 = 90
− 30− 30
10 x = 60
1 0 x = 6 0
÷ 10 ÷ 10
x = 6

33. Divide First
Solve the equation:
÷ 5 ÷ 5
− 6 − 6
÷ 2 ÷ 2

34. Independent Practice
Example 11:
8(3 x – 4)+ 5 x = 45
Which method will you
choose and why?
= 45
= 45
= 45
= 77
÷ 29 ÷ 29
= 2.66
I will choose
Expanding the
brackets method
, its easier in
calculations

35. Challenge Your self
Example 12:
-
-
-

36. -
x 40 x 40
3
3
− 8 − 8
3
÷ 3 ÷ 3

37. Plenary: Loop Cards
Have a go at the Unknowns
on Both Sides Loop Cards.

38. Exit Ticket
Example 12:
1 1

39. 9
4
t −
1
6
𝑡 =11+
6
4
9 × 3
4 × 3
t −
1 ×2
6 ×2
𝑡=
11 × 4
1 ×4
+
6 ×1
4 × 1
27
12
t −
2
12
𝑡 =
44
4
+
6
4
25
12
t =
50
4
25
12
t =
50
4
÷
𝟐𝟓
𝟏𝟐
x
t = 6
÷
𝟐𝟓
𝟏𝟐

40. Foldable Time
Go Mathematicians