SOLVING MULTI-STEP
EQUATIONS
C
Common Core Objective 8.EE.7
OBJECTIVE
I, THE STUDENT, WILL BE ABLE TO:
1.
SOLVE EQUATIONS WITH LINEAR
EXPRESSIONS WITH ONE
C
SOLUTION, INFINITELY MANY SOLUTIONS OR NO SOLUTIONS
(8.EE.7)
2.
GIVE EXAMPLES OF AND IDENTIFY EQUATIONS AS HAVING
ONE SOLUTION, INFINITELY MANY SOLUTIONS OR NO
SOLUTIONS (8.EE.7)
WARM UP – Thursday, October
Amy and Ben are trying to decide when the following equation is true:
th
16
5 −𝑥 =6
They decided to compare their work.
Amy:
5 −𝑥 =6
Ben:
If you take a number away from 5 the
so x = 6 – 5 = 1
answer will be less than 5, so it’s
so it is true when x = 1
never true.
Are Amy and Ben correct? If not, where have they gone wrong?
Amy: ________________________________________________________________
Ben: _________________________________________________________________
What is your answer to the question? _______________________________________
______________________________________________________________________
True or False?
4𝑥 + 1 = 3
Can you give me a value for x that makes this
equation false?
Show the calculations that explain your answer
by writing on your desk with a dry erase marker.
True or False?
4𝑥 + 1 = 3
Can you give me a value for x that makes this
equation true?
Show the calculations that explain your answer
by writing on your desk with a dry erase marker.
How many different values of x make
the equation true?
4𝑥 + 1 = 3
Cheryl: 𝑥 = 2
4 𝑥 2 + 1 = 9 (not 3)
𝑥=1
4 𝑥 1 + 1 = 5 (this doesn’t work)
𝑥=0
4 𝑥 0 + 1 = 1 (this doesn’t work)
𝑥=
1
2
1
+1
2
4𝑥
=3
There is only one value for x that makes
the equation true.
Stacey:
4𝑥 + 1 = 3
This means 4𝑥 = 2 and this
always has to be true. To
1
make 2, 𝑥 must be 2 because
4𝑥
1
2
=2
x can’t be any other value.
Collaborative Activity: Always,
Sometimes, or Never True? (30 Minutes)
• You will work in groups of three or four.
• Each group should have a Card Set: Equations, a pair of
scissors, a large sheet of paper, a marker, and a glue stick.
You will also need a pencil to use when writing your
explanations.
• You will be considering a number of equations in the same
way we have been solving equations. In your groups, you
will produce a poster that will show each equation classified
according to whether it is always, sometimes, or never true.
Always, Sometimes, or Never True?
• You will need to divide your sheet of paper into three
columns and head separate columns with the words:
Always True
Sometimes True
Never True
• What does always true mean?
• What does never true mean?
• How many examples does it take to prove that an equation is
sometimes true?
How will you work together?
1. One partner, selects an equation, cuts it out and places it in one of
the columns, explaining why you choose to put it there.
2. If you think the statement is sometimes true, give values of 𝑥 for
which it is true. If you think the equation is always true or never
true, explain how you can be sure this is the case.
3. Partners should challenge the explanation if they disagree OR
describe it in their own words if they agree.
4. Once you agree, stick the equation on the poster and write an
explanation on the poster in pencil next to the card.
5. Swap roles and continue to take turns until all equations are placed.
Sharing Posters (10 minutes)
1. Move to another table and look at their poster.
2. If you disagree with where an equation has been placed,
put a circle around the equation and write in pen:
• Why you disagree
• Which column you think the equation needs moving to.
• Why you think the equation belongs there.
3. Circle your comments and write your initials next to them.
Let’s Summarize (15 minutes)
Give me an equation that is always true/sometimes true/never true.
Why did you put this equation in this column?
Did anyone put this equation in a different column?
TICKET OUT!
Using your technology, you will answer 3 questions in google drive.
Go to my wiki page and click on the link under today’s
PowerPoint/date.
Please only respond once to the questions.
Your homework tonight is the half sheet titled: When are the
equations true?
Warm Up – Friday, October 17th
Solve the following equations:
1. 3𝑥 + 24 = 3 𝑥 + 8
2. 5 − 6𝑦 = 2 −3𝑦 + 1
3. − 2𝑏 + 8 = 2(𝑏 + 4)
1
4. 5
5𝑛 + 15 = 3𝑛 + 9