Transcript Solving Two Step Equations

Solving Two-Step Equations
Today’s Learning Goal

We will continue to use our understanding of inverse
operations to help us solve equations symbolically.
What does an inverse
operation do?

Consider the following situation:
You ride your bike north for 4 miles and decide that
you need to return to where you started. What do
you need to do to get back to where you started?
That’s right…ride your bike south 4 miles.

This is similar to solving the equation x + 4 = 11.
Because 4 was added to x to get 11, what needs to
be done to undo adding 4 to determine the value of
x + 4 = 11
the unknown?
–4 –4
Correct…subtract 4.
x = 7
Another concrete example of
inverse operations

When you were getting ready for school this
morning, most of you (still half asleep) put on your
socks and then your shoes. If you decided that you
wanted to change your shoes and socks, what would
you have to do to get back to bare feet?
Yes…take your shoes off first and then your socks.

In this example, the order in which actions were
done affected the order in which they were undone.
Inverse Operations



Like the socks and shoes example, the order in which
you undo the actions matters when dealing with
numbers.
For example, suppose you take an unknown number,
you multiply it by 4, and then you subtract 3 from the
total and you get 21.
What is the equation you can write for this statement?
Nice…4x – 3 = 21
Solving a Two-Step Equation

Given the equation below, what would we need to do
first to try to determine the unknown number?
Great…we need to add three first
because that was the last thing to
be done (shoes then socks).


Now we have an equation that
looks like one we know how to
solve. What would we do second
to solve for the unknown number?
Beautiful…divide both sides by 4.
4x – 3 = 21
+3 +3
4x = 24
4
4
x = 6
4(6) – 3 = 21
Don’t forget you can check your answer!
It works!
Another Example
What would be the equation for the following?
Take a number and multiply it by -3. Then add 6 to
the result to get 42.
-3x + 6 = 42
–6 –6
 What would you need to do
-3x = 36
first to undo what was done to
-3
-3
the unknown number?
x = -12
Fantastic…subtract 6 from both sides.

What do we do now to solve
for x?
Awesome…divide both sides by -3.

-3(-12) + 6 = 42
It works!
Solving Problems Using Equations


The following is a table of values for Alana’s pledge
plan including a $5 up-front fee plus $.50 per mile.
What is the equation
# ofmmiles Amount
of $
A
that would satisfy this
Collected
table of values if we let
0
5.00
m represent the number
of miles and A represent
1
5.50
the amount of money
2
6.00
collected?
3
6.50
Excellent…A = 5 + .5m
4
7.00
5
7.50
Solving Problems Using Equations




Given the equation below for Alana’s Pledge Plan,
what would we do first to determine how many miles
it would take to collect $8 from each sponsor?
Nice…plug in 8 for A.
8A = 5 + .5m
–5 –5
What is the first algebraic step
you should do to solve this
3 = .5m
problem?
 .5  .5
Great…subtract 5 from both sides.
6= m
What is the second algebraic
step to solve this equation?
8 = 5 + .5(6)
Beautiful…divide both sides by .5!
Don’t forget to check your solution!
It works!
Partner Work

You have 15 minutes to work on the following
questions with your partner.
For those that finish early
1. Five more than twice a number is 27. Write an
equation to solve for the unknown number.
2. Twelve year old Aaron O’Leary of Columbus, Ohio,
bought old bikes at an auction for $350. He fixed
them and sold them for $50 each. He made a
$6200 profit.
a) Write an equation for this situation that shows
the relationship between profit and the number of
bikes sold.
b) Determine how many bikes he sold using the
equation.
Big Ideas from Today’s Lesson


You use the inverse operations of addition and
subtraction, multiplication and division to solve
equations that involve two steps.
The order in which you undo the actions matters.
Homework


Complete Homework Worksheet
Pgs. 123 – 124 (13 – 37 odd, 47, 52, 53)