Transcript Solving Equations - Chuck Neuschafer

Solving Equations
M7A2b Use the addition and
multiplication properties of
equality to solve one- and
two-step linear equations.
What happened to the
order of operations?
Remember Please Excuse My Dear
Aunt Sally?
Parenthesis, Exponents, Multiply
and Divide, Add and Subtract
Well…..
Doesn’t it make sense that if we follow the
order of operations to find the answer…
that we do the order of operations
backward, to find part of the missing
problem when we already have the
answer?
For example:





Solve: 4(3) + 5 = x
First we’d multiply, then add 5. That
makes x equal 17.
What if you were given 4x + 5 = 17.
Can we multiply first then add?
Since we have the answer already, doesn’t
it make sense to work backward to find
the solution for x since x is the missing
part of the problem?
Inverse Operation
Suppose you were on the phone with your
friend who just gave you 20 numbers to
add into your calculator, the 21st number
she gave you was 15 but you accidentally
entered 115. Ooops! What can you do to
fix the problem?
Do you have to start all over again?
Applying the Inverse Operation



An operation’s inverse is the operation
that “undoes” the first operation.
For example, with the calculator problem,
if you accidentally added 115, you can get
back to where you were before you made
the error if you subtract 115.
Addition and subtraction are inverse
operations. What other two operations
are inverse operations?
Using Inverse Operation to Solve
Equations!
Ready, Set, Go!
Solve for x.
2(5x + 3) +4x -7 = 41
Just Kidding!
We must take it one little step at a time.
That is why we need to SHOW inverse
operation on both sides of the equation,
so we can see where we have been and
what we have already done.
Just nipping that question in the bud
before I hear it a thousand times.
Now for Real
Use inverse operation to solve the following
equation:
x + 6 = 10
Yeah, I know you know it is 4, but that’s not the
point. The point is, can you do and show
inverse operation on this small scale before you
have to do it on a big problem like the one I
showed you earlier, when whether you do it
correctly or not isn’t as obvious.
x + 6 = 10
The
inverse of addition is
subtraction, so subtract 6 from
each side to find the value of x.
x + 6 – 6 = 10 – 6
x=4
Check: 4 + 6 = 10
The solution is 4.
Now you try!
X + 3 = 12
Don’t forget to check!
Use addition to solve subtraction
problems.
x - 8 = 14
x - 8 + 8 = 14 + 8
x = 22
Check: 22 - 8 = 14
Now you try!
x – 12 = 13
Don’t forget to check!
Add or Subtract?
15 - x = 6
Ask yourself, was 15 subtracted from
anything? If we add 15, we’ll be
subtracting x from 30, not 0.
15 + 15 – x = 6 + 15
30 - x = 45
Wrong!
The Correct Way to
Do it!
15 - x = 6
15 – 15 – x = 6 - 15
- x = -9
So
x=9
Check: 15 – 9 = 6
Now you try!
20 – x = 16
Don’t forget to check!
Step-by-Step
1)
2)
3)
4)
Write the problem.
Show inverse operation on both sides of
the equation.
Solve.
Check.
Neat Points
Write
only one equal
sign on each line.
Line the equal signs up,
one under another.