Year 7 Equations
Objectives: (a) Solve equations, including with unknowns on both sides
and with brackets.
(b) Form equations from context (with emphasis on quality of written
communication, e.g. "Let x be...").
For Teacher Use:
Recommended lesson structure:
Lesson 1: Solving simple linear equations
Lesson 2: When variable appears on both sides/brackets
Lesson 3: Forming and solving equations from context.
Lesson 4: Introducing variables to solve equations.
Lesson 5: Solving Equations Levelled Activity (separate)
Lesson 6: Consolidation/Mini-assessment
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KEY TERMS
This is an example of a:
3
2𝑥
Term
3𝑥 + 2
Expression
2
5𝑥
+1=2
A term is a product of numbers
and variables
?
(no additions/subtractions)
An expression is composed
? of one or more
terms, whether added or otherwise.
Equation
An equation says that the
? expressions on the
left and right hand side of the = have the same
value.
STARTER
The perimeter of this
work of art is 32.
By trial and error (or any
other method), find 𝑛.
3𝑛 + 1
9−𝑛
𝑛=3
?
If we added all four sides of the painting to
get the perimeter, we’d have:
3𝑛 + 1 + 3𝑛 + 1 + 9 − 𝑛 + 9 − 𝑛
= 4𝑛 + 20
And we’re told the perimeter is 32, so
𝟒𝒏 + 𝟐𝟎 = 𝟑𝟐. We’ll see today how to
‘solve’ equations like this so we can find 𝑛.
Equations must always be ‘balanced’
We already know that the ‘=’ symbol means each side
of the equation must have the same value.
𝑎=4
+2
2 a
2 4
=
𝑎 + 2= 6
If we added something to one side of the equation,
what do we have to do with the other side?
+2
Equations must always be ‘balanced’
If we tripled the load on one side of the scales,
what do we have to do with the other side?
𝑎=4
×3
a
4
a a
4 4
=
×3
3𝑎 = 12
Solving
!To solve an equation means that we find the value of
the variable(s).
3𝑛 + 1
4𝑛 + 20 = 32
9−𝑛
Strategy: To get 𝑛 on its own on
one side of the equation, we
gradually need to ‘claw away’
the things surrounding it.
Solving
4𝑛 + 20 = 32
?
-20
?
-20
?
4𝑛 =
12
?
4
Strategy: Do the opposite
operation to ‘get rid of’ items
surrounding our variable.
𝑥+4
4?
? 3
𝑛=
Bro Tip: if we added something to one side of the
equation we must added it to the other side
3𝑦
𝑧
6
-4?
?
3
?
×6
𝑥
𝑦
𝑧
Test Your Understanding
3𝑛 − 5 = 13
?
+5
?
+5
3𝑛 = 18
?
?
3
?
3
?
𝑛=
6
When the solution is not a whole number
4 + 6𝑧 = 18
?
-4
-4?
6𝑧 = 14
?
?
6
6?
14 7
𝑧= ? =
16 3
Your Go…
3 = 20 + 4𝑥
−17 = 4𝑥
? 𝟏𝟕
𝒙=−
𝟒
Bro Note: In algebra,
we tend to give our
answers as fractions
rather than decimals
(unless asked).
And NEVER EVER EVER
recurring decimals.
Dealing with Fractions
𝑥
3 + = 28
5
?
-3
-3?
𝑥
? = 25
5
?
×5
?
×5
𝑥 = ?125
What step next?
Use your planners to vote for the step that
would be easiest to do next in solving the
equation.
×

+
-
2𝑥 + 7 = 5
-7
-7
2𝑥 = −2
×

+
-
3𝑥 = 9
3
3
𝑥=3
×

+
-
−1 + 7𝑥 = 13
+1
+1
7𝑥 = 14
×

+
-
𝑦
3
×3
×
=9
×3
𝑦 = 27

+
-
Multiplying by -1 or dividing by -1
would have the same effect.
−𝑥 = 2
(-1)
(-1)
𝑥 = −2
×

+
-
Exercise 1
Solve the following equations,
showing full working.
1
2
3
4
5
6
𝑛 − 4 = 10
2𝑥 + 3 = 9
5𝑥 − 4 = 36
9𝑥 − 2 = 61
9 = 1 + 4𝑦
8𝑎 + 3 = 75
7
3𝑥 = 7
8
5𝑥 + 2 = 11
9
8𝑥 − 2 = 3
10
3 + 10𝑞 = 7
11
5 + 3𝑎 = 4
12
7𝑏 + 23 = 11
13
14 + 9𝑏 = 3
𝒏 = 𝟏𝟒 ?
𝒙=𝟑 ?
𝒙=𝟖 ?
𝒙=𝟕 ?
𝒚=𝟐 ?
𝒂=𝟗 ?
𝟕
𝒙=
?
𝟑
𝟗
𝒙=
?
𝟓
𝟓
𝒙=
?
𝟖
𝟐
𝒒=
?
𝟓
𝟏
𝒂=− ?
𝟑
𝟏𝟐
𝒃=− ?
𝟕
𝟏𝟏
𝒃=− ?
𝟗
14
15
16
17
18
19
20
21
22
23
24
N
𝑥
=5
𝒙 = 𝟑𝟓 ?
7
𝑎
+3=8
𝒂 = 𝟐𝟎 ?
4
𝑏
−1=5
𝒃 = 𝟏𝟐 ?
2
𝑏
1+ =7
𝒃 = 𝟏𝟖 ?
3
𝑥
+3= 4
𝒙=𝟓 ?
5
𝑦
+8=5
𝒚 = −𝟏𝟐?
4
𝑎
5= +9
𝒂 = −𝟐𝟒?
6
2𝑥
3+
=7
𝒙 = 𝟏𝟎 ?
5
5𝑞
𝟕𝟖
?
− 3 = 10
𝒒=
6
𝟓
3𝑥
𝟖
5+
=3
𝒙=− ?
4
𝟑
6𝑥
𝟕
11 =
+9
𝒙=− ?
7
𝟑
6
𝑥+3
𝟖𝟓
5
3=
+9 𝒙=− ?
8
𝟐