Download Solving Equations with variables on both sides

BILL ME LATER
Chuck does simple carpentry jobs for his neighbors. He
charges $6.50 an hour for his labor and includes a flat
fee for each project’s supplies. He contracts with Mr.
Snow to build a set of shelves. At the end of the project,
he presents Mr. Snow with a bill for $112, which includes
$34 in supplies.
How many hours did Chuck spend on the project?
SOLVING EQUATIONS
WITH VARIABLES ON
BOTH SIDES
STUDENTS WILL APPLY THE USE OF THE DISTRIBUTIVE PROPERTY,
COMBINING LIKE TERMS AND THE MULTIPLICATIVE INVERSE TO SOLVE
EQUATIONS WITH VARIABLES ON BOTH SIDES OF THE EQUAL SIGN.
8.EE.7
WARM UP – MONDAY, OCTOBER 13TH
1. Write and solve an equation for: The sum of 6 and 2 times a
number is 24.
2. The perimeter of a rectangle is 72 inches. The length is 2 more
than the width. Write and solve an equation to find the dimensions.
3. Anzi’s Pizza charges $19 for a large pizza and $2.50 per topping. If
your total cost for a pizza is $29, how many toppings were on the
pizza?
4. The area of a rectangle is 44 ft2. Solve for x and find the length.
4
x+6
NOTES/STEPS TO SOLVING EQUATIONS
A quantity with a variable can be treated just like a quantity without
variables.
For example, we can add a quantity with a variable to both sides of an
equation without changing the equation of the value that make it true.
This is also true for subtracting.
HOW DO YOU DECIDE?
• The key to solving equations with variables on both sides of
the equation is to move all the terms containing the variable
to one, and only one, side. It doesn’t matter which side you
choose, just try to pick the easier one.
• How do you know which side is easier?
• I always move the smaller variable term first (but really, you
can do whatever you want – as long as you use inverse
operations)
EXAMPLE #1
15 − 𝑥 = 4𝑥
EXAMPLE #2
5𝑥 = 6 + 2𝑥
EXAMPLE #3
3𝑥 + 2𝑥 = 12 − 𝑥
EXAMPLE #4
5𝑦 − 3 = 3𝑦 + 5
EXAMPLE #5
8 −2 𝑥 −1 =𝑥 −8
EXAMPLE #6
2
1
𝑥 −1=9 − 𝑥
3
6
NOW, IT’S YOUR TURN…
THINK-PAIR-SHARE
3𝑦 − 3 = 6 𝑦 + 1
1

4
4𝑛 + 12 = 4 2𝑛 + 2
5 𝑥 − 5 + 3 = 𝑥 + 8
LET’S TRY A WORD PROBLEM TOGETHER
Green’s Gym charges a one time fee of $50 plus a $30
per session for a personal trainer. A new fitness center
charges a yearly fee of $250 plus $10 for each session
with a trainer. For how many sessions is the cost of
the two plans the same?
HOMEWORK
Use your notes and your textbook with the examples beginning on page
145 to help you.
To do: p.149 #1-8
p.151 #18-19
p.152 #22
OBJECTIVE
TUESDAY, OCTOBER 14TH
Students will continue with solving equations. These will involve the
distributive property, rational coefficients, variables on both sides and
some word problems . Some will include using shapes with equivalent
perimeters.
WARM UP – TUESDAY, OCTOBER 14TH
1. The length of a rectangular garden is 7 feet more than the width. The
perimeter is 50 feet. Find the width.
2. Solve:
𝑥 − 3 2𝑥 − 7 = 76
3. Write an equation and solve for x if the area of the rectangle is 55
square units.
5
3x - 1
4. The square and the triangle below have the same perimeter. What is
the value of x? What is the perimeter?
x+4
x
3x
x + 10
QUIZ THEN GALLERY CRAWL
 Quiz on solving equations
 Problem solving – PUNCHLINE p.52 (letters S, D, C, H, K, R)
PUNCHLINE p. 53 (numbers 5, 6)
 Gallery crawl of solving equations – answers sheets provided
(Students will complete a certain number of problems per each color)
 Homework – finish PUNCHLINE p. 52 (letters W, V, M, U, E, T, N)
finish PUNCHLINE p. 53 (numbers 3, 4, 7)
(These have a star by them)