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Linear Equations
What They Are
&
How to Solve Them
Definitions

Equation – A mathematical
sentence stating that 2
expressions are equal.
 12 – 3 = 9x
 8 + 4 = 12
 6x – 12 = 42
Definitions

Equals Sign (=) Means that the
amount is the same on both
sides.
4
+2=6
5 – 2 = 3
Definitions

Linear Equation –
 An
equation of the form:
ax + b = c
 14x + 3 = 17
An Equation is like a balance
scale. Everything must be
equal on both sides.
=
10
5+5
When the amounts are equal
on both sides it is a
True Equation or Identity.
=
12
6+6
When the amounts are
unequal on both sides it is a
False Equation or
Contradiction.
=
8
2+2
When an amount is unknown
on one side of the equation it is
an Open or
Conditional Equation.
=
7
n+2
When you find a number for n
you change the open equation
to a true equation.
You solve the equation.
=
7
5n + 2
Are these equations true, false
or open?
 11
-3=5
false
true
 13 + 4 = 17
open
N + 4 = 7
false
 12 – 3 = 8
 3 + v = 13
open
 15 – 6 = 9
true
Definitions

Inverse operation – the
opposite operation used to
undo the first.
4
+3=7
 6 x 6 = 36
7–4=3
36 / 6 = 6
How to solve an addition
equation
 Use the inverse operation for
addition, which is subtraction.
m + 8 = 12 8 is added to m
- 8 -8 Subtract 8 on both sides
m=4
How to solve a subtraction
equation
 Use the inverse operation for
subtraction, which is addition.
m - 3 = 5 3 is subtracted from m
+3 +3 Add 3 to both sides
m=8
Solve these equations using
the inverse operations
n
+4=7
n – 5 = 4
 n + 4 = 17
 n – 6 = 13
 n + 7 = 15
 n – 8 = 17
3
9
13
19
8
25
How to solve a multiplication
equation
 Use the inverse operation for
multiplication, which is division.
6m
=
12
m
is
multiplied
by
6
______
_____
6
6 Divide by 6 on both sides
m = 2
How to solve a division
equation
 Use the inverse operation for
division, which is multiplication.
m/3 = 4
m is divided by 3
3*(m/3) = 3*4 Multiply by 3, both sides
m = 12
Solve these equations using the
inverse operations
6
 3n = 18
20
 n/5 = 4
4
 4n = 16
 n/6 = 15
90
 7n = 35
5
 n/8 = 7
56
To solve equations 
Use the opposite operation


variable
alone
Do the same thing to both sides


to get the
to keep the balance
Bottom line:

X = a number