Question

Need help 10 mins, worth 40 points

answer the following:
How is an inequality different from an equation?
What are four ways an inequality can be written?
What would the graph of each inequality look like on a number line? (Use an example)
What would the graph of an equation look like on a number line? (Use an example)



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?



The table below shows the values of y for different values of x:

X | Y
0 | 0
1 | 4
2 | 8
3 | 12


Describe what happens when x increases by 1. Write this relationship as an equation.

What does it mean if a situation has a condition or constraint? Give an example.




Give an example of a situation that contains an independent and dependent variable. Explain if your data is continuous or discrete.


Sami earns $8.50 an hour walking dogs. Write an equation to represent this situation, be sure to define the variables.
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?

Answer 1

1. **Difference between an inequality and an equation:**
An inequality expresses a relationship between two quantities, indicating that they are not necessarily equal. It uses symbols like "<," ">", "<=" or ">=" to show the relationship. On the other hand, an equation represents a balance or equivalence between two expressions, where both sides are equal.

2. **Four ways an inequality can be written:**
- x < 5
- y ≥ -2
- 2a + 3b > 10
- 3x - 4y ≤ 12

3. **Graph of an inequality on a number line:**
For example, let's graph the inequality x ≤ 4 on a number line. You would represent all values of x that are less than or equal to 4, including 4 itself, by shading the region to the left of the point 4 on the number line.

4. **Graph of an equation on a number line:**
For example, let's graph the equation y = 2x - 3 on a number line. Since it's a linear equation, the graph will be a straight line. Plot points like (0, -3), (1, -1), and (2, 1) and draw a line passing through these points.

5. **Equation for finding the price of each bottle of water:**
Let's represent the price of each bottle of water as "p." The equation would be: 42p = $31.50

6. **Solving the equation:**
To find the price of each bottle of water, divide both sides of the equation by 42:
p = $31.50 / 42
p = $0.75
The price of each bottle of water is $0.75.

7. **Description of what happens when x increases by 1:**
When x increases by 1, y also increases by 4. This relationship can be written as an equation: y = 4x

8. **Situation with a condition or constraint example:**
If a situation has a condition or constraint, it means there are certain limitations or restrictions on the variables involved. For example, consider a budgeting scenario where you can spend a maximum of $200 on groceries each month. Here, the condition is the budget constraint of $200.

9. **Example of a situation with independent and dependent variables:**
Situation: The number of hours (independent variable) a student studies affects their test score (dependent variable). The data here is continuous because studying for any fraction of an hour can have an impact on the test score.

10. **Equation to represent Sami's situation:**
Let h represent the number of hours Sami walks dogs, and E represent her earnings. The equation would be: E = 8.50h

11. **Sami's earnings for 10 hours of dog walking:**
E = 8.50 * 10
E = $85.00
Sami will earn $85.00 if she walks dogs for 10 hours a week.

12. **Time needed to earn $102.00:**
102 = 8.50h
h = 102 / 8.50
h = 12 hours
Sami will need to walk dogs for 12 hours to earn $102.00.