Date: May 14, 2023

# Worksheet Test

Directions: Choose the correct answer for each question.

## Part 1: Basic Concepts

1. What is a fractional inequality?
2. How do you solve a fractional inequality?
3. What is the difference between a proper and an improper fractional inequality?
4. What is the difference between a strict and a non-strict fractional inequality?

## Part 2: Solving

1. Solve the following fractional inequality:

``(2x + 5)/(x - 3) >= 0``
2. Solve the following fractional inequality:

``(3x - 4)/(x + 2) < 0``
3. Solve the following fractional inequality:

``(4x - 7)/(2x + 3) > 5``
4. Solve the following fractional inequality:

``(x - 1)/(2x - 3) < -2``

## Part 3: Graphing

1. Graph the solution set for the following fractional inequality:

``(x - 2)/(x + 3) >= 0``
2. Graph the solution set for the following fractional inequality:

``(x - 4)/(x - 6) < 0``
3. Graph the solution set for the following fractional inequality:

``(3x - 1)/(2x + 5) > 0``
4. Graph the solution set for the following fractional inequality:

``(4 - x)/(x - 2) <= -3``

## Part 4: Applications of

1. A carpenter needs at least 5 pieces of wood that are each more than 3 feet long. If the carpenter has a total of 25 feet of wood, what is the maximum length of each piece of wood?
2. A furniture store offers a discount of 20% on all purchases over \$100. If a customer spends \$250, what is the maximum discount they can receive?
3. A manufacturer produces two models of a product, A and B. Model A requires 2 hours of machine time and 1 hour of labor time, while model B requires 1 hour of machine time and 3 hours of labor time. The manufacturer has 80 hours of machine time and 90 hours of labor time available each day. What is the maximum number of each model that can be produced each day?

## Part 5: Challenge Questions

1. Solve the following fractional inequality:

``(x - 2)/(x + 1) + (x - 4)/(x - 3) < 0``
2. Solve the following fractional inequality:

``(x - 1)/(x - 2) - (x + 3)/(x + 4) > 0``
3. Graph the solution set for the following fractional inequality:

``(3x - 2)/(x + 1) - 2 > (x - 5)/(x - 2)``
4. Graph the solution set for the following fractional inequality:

``(x - 3)/(x + 2) + (x - 1)/(x - 4) < (x + 5)/(x - 1)``
5. Write a real-world scenario that can be modeled by a fractional inequality and solve it.

1 A.
2 A.
3 A.
4 A.
5 A.
6 A.
7 A.
8 A.
9 A.
10 A.
11 A.
12 A.
13 A.
14 A.
15 A.
16 A.
17 A.
18 A.
19 A.
20 A.