Basic rules for Solving an Equation

1. 2a + 7
a 7 2
x - 3
x -3 1
3y - 7
y -7 3
3a + 16
a 16 3
2n - 9
n - 9 2

2. The Four Basic Rules for Solving an Equation
1. Addition Property of Equality
If the same quantity is added to both sides of an
equation, the resulting equation is equivalent to
the original equation.
Example: x–6=16 add (+6) to both sides
x–6+6 = 16+6
x = 22
-6+6=0 16+6=22

3. 1. x-3 = 7
2. y 5 =10
−
3. a-4 =12
4. x-2 = 10
5. z-6 = 7

4. 2. Subtraction Property of Equality
If the same quantity is subtracted from
both sides, the resulting equation is
equivalent to the original.
Example: x + 6= 16 subtract both sides by
(-6)
x+6–6 = 16-6
x = 10
6-6=0 16-6=10

5. 1. x+5 = 10
2. y+3 = 8
3. x+6 = 15
4. z+8 = 10
5. a+5 = 20

6. 3. Multiplication Property of Equality
If both sides of an equation are
multiplied by the same (nonzero)
quantity, the resulting equation is
equivalent to the original equation.
Example: = 15 multiply both sides
by 5
5 = 15 515x5=75
5 is cancelled
out
X = 75

7. 1. 2.
5.
4.
3.

8. 4. Division Property of Equality
If both sides of an equation are divided by
the same (nonzero) quantity, the
resulting equation is equivalent to the
original equation.
Example: 5x =15 divide both sides by
5
= X = 3

9. 1. 5x = 25
2. 12y = 48
3. −6z = 42
4. 3a = 21
−
5. −8b = 64
−

10. Let’s try to translate and solve the following equation:
I am six years older than twice the age of my youngest sister. If I
were 66 years old. How old is my youngest sister?
Twice the age (2n) + six years older (+6) = 66 years old
2n + 6 = 66

11. Let’s try to translate and solve the following equation:
I am six years older than twice the age of my youngest sister. If I
were 66 years old. How old is my youngest sister?
Twice the age (2n) + six years older (+6) = 66 years old
2n + 6 = 66
2n + 6 – 6 = 66 -6 (Subtraction Property of Equality) -6
2n = 60
2 2
(Division Property of Equality) /2
N = 30

12. 1.2x + 4 = 16
2.68 = 3y – 4
3. = 17
4. = 7
5. 5y + 0 = 125
Solve the following equation using the 4
basic rule in solving equation.

13. 1. I am 24 years old. My age is 2 less than twice
my sister’s age.
2. Arvin has a bake shop. He sold 85 cakes today.
That is 16 cakes fewer than yesterday. How many
cakes did he sell yesterday?
3. Ann have 56 stamps that are 6 less than one-
half of my stamps. How many stamps do I have?
Translate each problem into a mathematical
equation then solve: