Real World Scenarios
Sylvester and Erin collect baseball cards. Sylvester has 250 baseball cards and collects 15 cards per week. Erin has 300 baseball cards and collects 5 cards per week. After how many weeks will Sylvester and Erin have the same number of baseball cards?
5 weeks
32x<9−6x32x<9-6x
x < 6/5
How many solutions does the following have:
2(5x+3)=6(x+8)+2
One solution
−2.7x+3.5=1.3x+11.5
-2
What is the first step for solving a multistep equation?
Distribute
The equation 3x+5=2x+7 represents the cost in dollars, x, of a school lunch. What is the cost of the school lunch?
$2
−2x−9≤5
x > -7
How many solutions does the following have:
3(4x-4)=4(3x-3)
Infinite solutions
10(x+6.25)<111
x < 4.85
What is the second step for solving a multi-step equation or inequality?
Combine like terms
A group of 7 students went bowling. Each student rented bowling shoes and spent $15 on snacks. A group of 6 adults went bowling and paid twice as much to rent bowling shoes as each student. Each adult also spent $12.50 on snacks. If both groups spent the same total amount, what was the cost for each adult to rent bowling shoes?
$12
−3x−3>12
x < -5
How many solutions does the following have:
4(x-5)=2(9+2x)
No solutions
−2(4x+6)+4=2(5x−9)−8x
1
What is the third step in solving a multistep inequality?
Inverse operations
The temperature of one furnace is 1,400ºC and cools at a rate of 2.5ºC per minute. The temperature of another furnace is 1,200ºC and is heated at a rate of 1.5ºC per minute.
After how many minutes will the furnaces be the same temperature?
50
6.5x−11.3 ≤8.2
x ≤ 3
How many solutions does the following have:
4(x−8)+12=2(2x−9)
No solution
−g+2(3+g)=−4(g+1)
-2
What is the fourth step in solving a multistep inequality?
Graph
Marko has 45 comic books in his collection, and Tamara has 61 comic books. Marko buys 4 new comic books each month and Tamara buys 2 comic books each month. After how many months will Marko and Tamara have the same number of comic books?
Let m represent the number of months. Write an equation to represent the situation.
45 + 4m = 61 + 2m
When do we use a closed circle?
When it has the line underneath (or equal to)
Complete the equation so that is has infinitely many solutions.
2x-7(x+10) = ___x + ____
2x-7(x+10)= -5x + -70
−8−x=−3(2x−4)+3x
10
How do we know which way to shade our answer.
Less than (left) <, <----------
Greater than (right) >, ----------->