Transcript 6.1 Solving Equations by Using Inverse Operations

To ‘undo’ a sequence of operations…
… we perform the inverse operations in the reverse
order.
For example, compare the steps and operations to wrap
a present with the steps and operations to unwrap the
present:
1. Put present in
box
2. Wrap box
3. Put on ribbon
3. Take present
out of box
2. Unwrap box
1. Take off
ribbon
Inverse Operations…
… ‘undo’ or reverse each other’s results.
In order to be able to solve equations, you
MUST know the mathematical inverse
operations:
We can use inverse operations to
solve equations…
… to do this, we determine the operations that
were applied to the variable to build the
equation.
We then use INVERSE OPERATIONS to
isolate the variable by ‘undoing’ these
operations.
Here’s an example…
x  5  13
What mathematical
operations have been
applied to the variable to
build this equation?
+5
BUILD
What is the
inverse
operation?
SOLVE
-5
Let’s look at a few more examples:
3  x  9
7t  21
BUILD
SOLVE
What does the ‘math’ look like when we solve these equations?
Let’s try a harder one…
4 .5 d  3 .2   1 8 .5
x 4.5
- 3.2
BUILD
SOLVE
÷ 4.5
Inverse Operations!
+ 3.2
How can you
check to see if
you are correct?
Here’s a few more…
Make sure you ‘build’ the equation first and then use the inverse to solve!
m
 1.5
4
r
4
 3  7.2
Have you noticed a
connection between
solving equations and
BEDMAS?
Here’s the hardest one yet!
+1
x7
÷2
( 2 ) 7 ( x  1)
7 ( x  1)
2
-1
÷7
x2
 14 ( 2 )
2
7 ( x  1)  28
7
7
( x  1  1)  4  1
x 3
The KEY thing to remember about solving any equation is:
Whatever you do to one side of an equation, you must do
to the other side to keep the equation balanced!
How about a ‘word problem’? 
A rectangle has length 3.7 cm and perimeter
13.2 cm.



Write an equation that can be used to determine the
width of the rectangle.
Solve the equation.
Verify (check) your solution.
Working with %...
Seven percent of a number is 56.7.


Write, then solve an equation to determine the
number.
Check the solution.
What does
OF mean in
math?
Choose the method
that works best for
you, but you MUST
show an equation!
Page 271: 5ab, 6ac, 7 (discuss), 8be, 9ab, 10bcf, 11ad, 12
(discuss), 13abc, 14abc, 16ab, 17ab, 18acd (be
prepared to go over in class!)
What are the rules for solving
equations?
Build the equation (either on paper) or in your
mind.
Whatever operation you do to one side, you
MUST do to the other side in order to keep the
equation balanced!
ALWAYS CHECK YOUR WORK!