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Semester 2
Warm Up
1.5𝑥=20
2 .12+𝑥2=15
3 .−2 ( 𝑥+9 )=−10
𝑥=4
𝑥=6
𝑥=−4
𝑥=2
Objective: SWBAT solve multi-step equations.2.4.d.ii
DOL: Given 3MC and 1 CR question, SW solve multi-step equations with 100% accuracy.
Essential Question How can we create equations to solve
problems?
Why?We’re starting the semester with systems
of equations, where we’ll need to use multiple equations to each problem.
Variable: A symbol for a number we don’t know yet Coefficient: A number multiplied by a variable Like terms: Terms with the same variables and powers
I used the variable ___. ____ is like terms with ____ because…
d8
p10w4
w2p12
t4
d2
p7w13
p
w3
d5
Combining Like Terms
Variable: A symbol for a number we don’t know yet Coefficient: A number multiplied by a variable Like terms: Terms with the same variables and powers
When we combine all like terms with the variable ______, we get _____
d8p10w4
w2p12
t4
d2p7
w13
p
w3
d5
Combining Like Terms
Combining Like Terms
We can simplify expressions by combining like terms
Examples:
What’s the rule for combining like terms?Show you know:
Combining Like Terms
We can simplify expressions by combining like terms
Examples:
To combine like terms, add or subtract the coefficients
Whiteboard check
Heating Up On Fire
Distributive Property
We can simplify expressions by using the distributive property
Examples:
What’s the rule for distribution?Show you know:
Distributive Property
We can simplify expressions by using the distributive property
Examples:
What’s the rule for distribution?
Show you know:
We Do
Whiteboard check
Heating Up On Fire
Independent Work
Heating Up On Fire
Independent Work
If you feel comfortable with a section, skip ahead to the next one
Beating the Competition
About 4.9 million households had computer Brand A. The use of Brand A grew at an average rate of 0.275 million households a year. In 2001, about 2.5 million households used Brand B computers. The use of Brand B computers grew at an average rate of 0.7 million households a year. How long will it take for the two types of computer to be in the same number of households? What year is this?
Beating the Competition
About 4.9 million households had computer Brand A. The use of Brand A grew at an average rate of 0.275 million households a year. In 2001, about 2.5 million households used Brand B computers. The use of Brand B computers grew at an average rate of 0.7 million households a year. How long will it take for the two types of computer to be in the same number of households? What year is this?
4.9 + 0.275y = 2.5 + 0.7yY = 5.6 yearsThis will happen in the year 2006
Dishing It Up
Moe Tell starts washing dishes at the Greasy Spoon Café. Fifteen minutes later Fran Tick joins Moe, and both wash until all the dishes are done. Moe washes 9 dishes per minute and Fran washes 16 dishes per minute. Together, they need to wash 760 dishes.
Write an equation that can represent the total number of dishes washed.
Dishing It Up
Moe Tell starts washing dishes at the Greasy Spoon Café. Fifteen minutes later Fran Tick joins Moe, and both wash until all the dishes are done. Moe washes 9 dishes per minute and Fran washes 16 dishes per minute. Together, they need to wash 760 dishes.
Moe: dishes per minute
Fran: dishes per minute, but only after 15 minutes
Final equation:
Plumbing Out
Nick O’Time, the plumber, charges $30 per hour. His brother Ivan, the plumber’s helper, charges $20 per hour. Nick starts working on a job. Four hours later Ivan joins him and both work until the job is finished. They want to earn at least $470.
Write an inequality to represent how much they make based on how many hours they work.
Plumbing Out
Nick O’Time, the plumber, charges $30 per hour. His brother Ivan, the plumber’s helper, charges $20 per hour. Nick starts working on a job. Four hours later Ivan joins him and both work until the job is finished. They want to earn at least $470.
Nick: per hour
Ivan: per hour, but starts 4 hours later
Final equation:
On the Run
A cougar spots a fawn 132 meters away. The cougar starts toward the fawn at a speed of 18 meters per second. At the same instant the fawn starts running away at 11 meters per second.
Write an equation to determine how long it will take for the cougar to catch the fawn.
On the Run
A cougar spots a fawn 133 meters away. The cougar starts toward the fawn at a speed of 18 meters per second. At the same instant the fawn starts running away at 11 meters per second.
Cougar:
Fawn:
Final equation:
The cougar closes in at 7 meters per
second.The cougar catches the fawn
after 19 seconds…if it can hold that speed.
DOL
DOL
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