Here are answers to your questions:
How is an inequality different from an equation?
An inequality has a symbol like <, >, ≤, or ≥ indicating that the quantities on either side of the symbol are not equal, while an equation has an = sign indicating the quantities are equal.
What are four ways an inequality can be written?
x > 5
x ≥ 5
5 < x
5 ≤ x
What would the graph of each inequality look like on a number line? (Use an example)
x > 5 would look like a number line with a circle at 5 and all numbers to the right in an open circle
What would the graph of an equation look like on a number line? (Use an example)
x = 5 would look like a number line with a solid circle at 5
The soccer team raised $31.50 by selling 42 bottles of water. Write an equation with a variable that can be solved to find the price of each bottle of water. Solve your equation. How do you know your answer is correct?
p = price of 1 bottle
42p = 31.50
p = 31.50/42 = $0.75
I know it's correct because when I multiply 0.75 by 42 I get 31.50.
Describe what happens when x increases by 1. Write this relationship as an equation.
y increases by 4. The equation would be y = 4x
What does it mean if a situation has a condition or constraint? Give an example.
It means there is a limitation or rule that must be met. For example, if you have $50 to spend, that is a constraint or condition on how much you can purchase.
Give an example of a situation that contains an independent and dependent variable. Explain if your data is continuous or discrete.
The amount of time spent studying (independent variable) and test score (dependent variable). The data would be discrete since time is measured in discrete units like hours and test scores are whole numbers.
Sami earns $8.50 an hour walking dogs. Write an equation to represent this situation, be sure to define the variables.
h = hours worked
earnings = 8.50h
How much will Sami earn if she walks dogs for 10 hours a week? How long will she need to walk dogs to earn $102.00?
For 10 hours, earnings = 8.50(10) = $85
To earn $102, 102/8.50 = 12 hours