Quiz: Inequalities and Their Graphs

Question

MS: Pre-Algebra A [M] (Sequential) (GP) / 4:Solving Equations and Inequalities answers

Answer 1

Sure! I can help you understand inequalities and how to graph them. Below is a quiz on inequalities along with answers and explanations.

Quiz: Inequalities and Their Graphs

1. Answer the following inequality question: Solve for \( x \):
   \( 3x - 4 > 5 \)

   a) \( x > 3 \)
   b) \( x < 3 \)
   c) \( x > 2 \)
   d) \( x < 2 \)

   Answer:
   To solve \( 3x - 4 > 5 \):
   Add 4 to both sides:
   \( 3x > 9 \)
   Divide both sides by 3:
   \( x > 3 \)
   Correct answer: a) \( x > 3 \)

2. What is the solution set for the inequality: \( 5x + 2 \leq 17 \)

   a) \( x \leq 3 \)
   b) \( x \geq 3 \)
   c) \( x < 3 \)
   d) \( x > 3 \)

   Answer:
   To solve \( 5x + 2 \leq 17 \):
   Subtract 2 from both sides:
   \( 5x \leq 15 \)
   Divide by 5:
   \( x \leq 3 \)
   Correct answer: a) \( x \leq 3 \)

3. Graph the inequality:
   \( x < -1 \)

   Answer:
   To graph \( x < -1 \):
   Draw a number line. Place an open circle at -1 (not included), and shade to the left (less than).

4. Solve and graph the inequality:
   \( -2x + 3 \geq 7 \)

   a) \( x \leq -2 \)
   b) \( x \geq -2 \)
   c) \( x < -2 \)
   d) \( x > -2 \)

   Answer:
   To solve:
   Subtract 3 from both sides:
   \( -2x \geq 4 \)
   Divide by -2 (remember to flip the inequality sign):
   \( x \leq -2 \)
   Correct answer: a) \( x \leq -2 \)
   Graph: Open circle at -2, shaded to the left.

5. Which of the following inequalities represents all numbers greater than or equal to 4?

   a) \( x > 4 \)
   b) \( x \geq 4 \)
   c) \( x < 4 \)
   d) \( x \leq 4 \)

   Answer:
   Correct answer: b) \( x \geq 4 \)

Conclusion

Feel free to ask if you have specific questions or need further explanations about inequalities and their graphs!