Math 6High (Period 3)

Solving Addition Equations 5.3

Although you are very capable of doing many of these equations in your head, this lesson is about the process à rather than just getting the correct solution.

n + 8 = 17

The goal of solving equations is to isolate the variable on one side of the equation (all alone on one side of the equals sign)

To do that we use inverse operations. Inverse operations are operations that “undo” each other, such as addition and subtraction.

Subtraction Property of Equality

Subtracting the same number for EACH SIDE of an equation produces a new equation having the same solution as the original.

x + a = b  à x + a  - a = b -a

So  with n + 8 = 17

We need to isolate n from EVERYTHING else.

Since currently 8 is being added to our variable, we need to undo addition. The Inverse Operation we will use is subtraction. BUT, we need to subtract 8 from BOTH SIDES OF THE EQUATION.

Formal Check is easy:
Rewrite the equation first
Substitute in your solution for n  written in (hugs) Put a “?” over the equals sign at this point.
DO THE MATH… that is…   Make sure the left side = the right side

n  + 8 = 17

(9) + 8 = 17

17 = 17

What about the following

x + 9 = 4

To isolate the variable, we need to undo addition again. We need to subtract 9 from both sides of the equation.

x =  -

But wait!

Look at the right side of the equation now! We have different signs for Integers. We must follow the rules for Different Signs. First we determine who has the larger absolute value ( That’s our “who wins?”) We stack the winner on top. We know that our solutions MUST include a NEGATIVE. so let’s set up the solution with x = -    so we don’t forget.

Then after stacking the winner on top, we take the difference and discover that x = -5

FORMAL CHECK:

Rewrite the original equation
Substitute in our solution using (hugs)
DO THE MATH

x + 9 = 4

(-5) + 9  = 4

Use a side bar to check -5 + 9

We have different signs here as well. Who wins? The +9, by how much?

Stack them

so

x + 9 = 4

(-5) + 9 = 4

4 = 4

We did the following in class

n + 8 = -2

4 = x + 9

-12 = 11 + p

46 + b = -4

n + 7 = -7

You will be required to show all the balancing stepsà even f you could do these equations in your head.

You will also need to do a Formal Check for a few of the problems.