Inequalities & Equations
Number Lines
Equivalent Equations
Factor Expressions
Surprise
100
A trailer will be used to transport several 40 kilogram crates to a store. The greatest amount of weight that can be loaded on the trailer is 1,050 kilograms. An 82 kilogram crate has already been loaded onto the trailer.
What is the greatest number of 40 kilogram crates that can also be loaded onto the trailer?
24 40 Kilogram crates
40x + 82 < 1,050
100
Find the values that will make true and show them on a number line.
x > -5
100
Write an equivalent equation for x2 + 3x + 2x +4 +2x2 +5 = 35
3x2 + 5x + 9 = 35
100
Factor 18y - 36
18(y - 2)
100
Simplify: 7π β 8 β 12π + 4
-5a - 4
200
A museum opened at 8:00 am. In the first hour, 350 people purchased admission tickets. In the second hour, 20% more people purchased admission tickets than the first hour. Each admission ticket costs $17.50.
What was the total amount of money paid for all the tickets purchases in the first two hours?
$13,475.00
((350 x .20) + 350) + 350 = x
17.50x
200
Find the values that will make true and show them on a number line.
x less than or equal to -2
200
Complete the equation with numbers that make the expression on the right side of the equal sign equivalent to the expression on the left side.
40a + 5b = 5(8a + b)
200
Factor 63z2 + 7z - 7
7(9z2 + z + 1)
200
Solve the equation.
β4π₯ β 5 = 7
x = -3
300
When Keisha installed a fence along the 200 foot perimeter of her rectangular back yard, she left an opening for a gate. In the diagram below, she used π₯ to represent the length, in feet, of the gate.
What is the value of x?
10 feet
300
On a number line, show all the values of π‘ that make this inequality true. 6 - 2t < -4
300
Write an expressions that is equivalent to 6π₯ + 1 β (3π₯ β 1).
6π₯ + β3π₯ + 1 + 1
3π₯ + 2
6π₯ + 1 + (β3π₯) β (β1)
300
Factor 25y - 15
5(5y - 3)
300
Simplifying the expression 6 β 2π₯ + 5 + 4π₯
2x + 11
400
At midnight, the temperature in a city was 6 degrees Celsius. The temperature was dropping at a steady rate of 2 degrees Celsius per hour.
Create an inequality that represents π‘, the number of hours past midnight, when the temperature was colder than -4 degrees Celsius.
6 - 2t < -4
400
Write a number line that shows all the values of π₯ that make the inequality β3π₯ + 1 < 7 true?
400
Write an equation to match the diagram.
3(π₯ + 6) = 30
3π₯ + 18 = 30
400
Factor to create an equivalent expression:
4(9a - 4)
400
Solve the equation.
y = -4
500
Lin got a $50 gift card to an online music store. She uses the gift card to buy an album for $9.99. She also wants to use the gift card to buy some songs. Each song costs $1.29.
Write an inequality that describes this situation, where π is the number of songs Lin wants to buy
9.99 + 1.29π β€ 50
500
Expand to create an equivalent expression:
2x - 3y
8/4x - 12/4y
500
Factor (β18) β 64π
-2(9 + 32n)
2(-9 - 32n)
500
Priya, Han, and Elena, are members of the running club at school. Priya was busy studying this week and ran 7 fewer miles than last week. She ran 9 times as far as Elena ran this week. Elena only had time to run 4 miles this week.
How many miles did Priya run last week?
Write an equation to solve this problem
43 Miles
x + 7 = 36