Math 6 H Periods 1, 6 & 7 (Monday)

Equations: Addition and Subtraction 8-2



If the replacement set for an equation is the set of whole numbers, it is not practical to use substitution to solve the equation. Instead we transform or change the given equation into a simpler, equivalent equation. When we transform the given equation, our goal is to arrive at an equivalent equation of the form
variable = number

for example

n = 5

the number 5 is then, the solution of the original equation. The following transformations can be used to solve equation

Transformation by addition: add the same number to both sides
Transformation by subtraction: subtract the same number from both sides

solve x – 2 = 8

our goal is to find an equivalent equation of the form

x = a number

The left side of the given equation is x – 2. Recall that addition and subtraction are inverse operations. If we add 2 to both sides the left sides simplifies to x

x-2 = 8
x – 2 + 2 = 8 + 2 (We usually show the +2 right below each side of the equation)
x = 10

The solution is 10

Solve x + 6 = 17

Subtract 6 from both sides of the equation to get an equivalent equation of the form “ x = a number”

x + 6 = 17
x + 6 – 6 = 17 – 6 (Again, we usually show the -6 right below each side of the equation)
x = 11
the solution is 11

In equations involving a number of steps, it is a good idea to check your answer. This can be done easily by substituting the answer in the original equation.
What about the following

34 – x = 27

add x to both sides

34 – x + x = 27 + x
34 = 27 + x
subtract 27 from both sides

34 – 27 = 27 – 27 + x
7 = x

You may be able to solve some of the equations in the homework without pencil and paper. Nevertheless, it is important to show all the steps in your work and to make sure you can tell which transformation you are using in each step.

Which transformation was used to transform the first equation into the second

x – 3 = 5
x – 3 + 3 = 5 + 3


Remember when we stated the properties as well-- back in our 1st quarter!!