Math 7 B Inequalities Unit Test

Answer 1

I can help you prepare for your Math 7 inequalities unit test! Here are some common concepts and sample questions related to inequalities that you might encounter:

Key Concepts

1. Inequality Symbols:

   • Greater than (>)
   • Less than (<)
   • Greater than or equal to (≥)
   • Less than or equal to (≤)

2. Graphing Inequalities:

   • Use open circles for < and > (not including the endpoint)
   • Use closed circles for ≤ and ≥ (including the endpoint)

3. Solving Inequalities:

   • Similar to solving equations, but when you multiply or divide both sides by a negative number, you must reverse the inequality sign.

4. Compound Inequalities:

   • "And" statements (e.g., x > 2 and x < 5)
   • "Or" statements (e.g., x < 1 or x > 3)

Sample Questions

1. Solve the Inequality:
   \( 5x - 7 \leq 18 \)
   Answer: \[ 5x \leq 25 \implies x \leq 5 \]

2. Graph the Solution:
   Graph the solution to \( x > 3 \) on a number line.

3. Write the Compound Inequality:
   Write the compound inequality for the statement: "x is more than 2 but less than 5."
   Answer: \( 2 < x < 5 \)

4. Solve the Compound Inequality:
   \( -2 < 3x + 1 \leq 8 \)
   Step 1: Solve the left side:
   \(-2 < 3x + 1\)
   \(-3 < 3x\)
   \(-1 < x\) (or \( x > -1\))

   Step 2: Solve the right side:
   \(3x + 1 \leq 8\)
   \(3x \leq 7\)
   \(x \leq \frac{7}{3}\)

   Final Answer:
   \(-1 < x \leq \frac{7}{3}\)

5. True or False:
   If \( x > 4 \), is it true that \( x + 2 > 6 \)?
   Answer: True, because if \( x > 4\), then \( x + 2 > 6\).

Practice Problems

Try solving these practice problems:

1. Solve and graph the inequality:
   \( 4x + 3 > 19 \)

2. Solve the compound inequality:
   \( -5 \leq 2x - 1 < 7 \)

3. Determine if the following statement is true:
   If \( x < 10\), is \( 2x < 20\)?

4. Express the following scenario as an inequality:
   "A number \( y \) is at least 12."

Review

• Make sure you understand each step when solving inequalities.
• Practice graphing to clearly visualize the solution sets.
• Pay attention to details, especially when multiplying or dividing by negative numbers.

If you have specific problems or topics you'd like help with, feel free to ask! Good luck on your test!