two step equations(3.1)
What is the first step in a 2-step equation
Isolate the variable
What property do you use when you rewrite the equation 6(x + 1) = 12 as 6x + 6 = 12.
Distributive property
what steps would you take to solve 8x + 5 = 2x -7
Isolate the variable terms, isolate constant terms, solve for x
What are equivalent inequalities?
different ways of writing the same mathematical relationship
Which property would you use to solve the inequality -7y ≤ 49?
division property of iniquality
If the number connected to the variable is positive, what would you do to it
subtract the number
Identify the like terms you would combine to solve the equation. -3x + 5 - 2x + 8 = 12.
-3x and 2x, 5 and 8
Explain why the equation 5z + 2 = 5z has no solution.
because you can't do it without z anceling out
Explain how the graph of x > 5 is different from the graph of x ≥ 5.
because x ≥ 5 means more than or equal to 5 rather than just more than 5
8b > 32
b > 4
Solve:
12k + 7 = 31
k = 2
Solve:
3(x + 1) = 6
1
Solve:
13m - 22= 9m - 6
4
Tell whether the given number is a solution of 5 < n (in order)
8, -8, -4, 4
yes, no, yes, yes
-3r ≥ 21
r ≤ -7
Solve:
7s + 5 = 40
s = 5
16 = 8(x - 1)
3
15 - 4x = 42 - 7x
9
Solve:
x + 2 > -3
x > -5
Explain how solving 2x > -14 is different from solving -2x > 14.
On the second one, you have to flip the inequality sign
A group of 9 friends takes a white-water rafting trip. the total price of the trip before any discounts is $810. each person in the group receivs a student discount. the total price with the dicount is $729. how much is the dicount per person.
each student gets a dcount of $9
You want to organize a group of friends to go to a karaoke studio this Friday night. You must pay $30 to reserve a private karaoke room plus $5 for each person in the group. You also want to have snacks for the group for $2 per person. How many people can be in the group if you have $70 to spend?
5 people
Spanish Club The Spanish clubis arranging a trip to a Mexican restaurant in a nearby city. Thosewho go must share the $60 costof using a school bus for the trip. The restaurant’s buffet costs $5per person. How many students must sign up for this trip to limit the cost to $10 per student? In Example 2, you will see how to use an equation to answer thisquestion.
12 students
You are competing in a triathlon, a sports competition with three events. Last year, you finished the triathlon in 85 minutes. The table shows your times forthis year’s first two events. What possible times can you post in the running event and still beat last year’s finishing time? (swimming time = 45 mins, biking time = 17 mins)
t < 23
You want to use in-line skates. You can either rent in-line skates for $12 per day or purchase them for $60. How many times will you have to use the in-line skates in order for the cost of purchasing them to be less than the total cost of renting them?
at least 6 times