8th Grade Linear Inequalities Test Prep & Review

📚 Quick Study Guide

• 🔢 Definition: A linear inequality is a mathematical statement that compares two expressions using inequality symbols.
• ⚖️ Inequality Symbols:
  • $>$ (greater than)
  • $<$ (less than)
  • $\geq$ (greater than or equal to)
  • $\leq$ (less than or equal to)
• ✍️ Solving Linear Inequalities:
  • Isolate the variable using addition, subtraction, multiplication, and division.
  • Remember to flip the inequality sign when multiplying or dividing by a negative number.
• 📈 Graphing on a Number Line:
  • Use an open circle (o) for $>$ and $<$.
  • Use a closed circle (•) for $\geq$ and $\leq$.
  • Shade the number line in the direction of the solutions.
• 📝 Compound Inequalities: Inequalities joined by "and" or "or". Solve each inequality separately and then combine the solutions.
  • "And" (Intersection): The solution includes values that satisfy both inequalities.
  • "Or" (Union): The solution includes values that satisfy either inequality.

🧪 Practice Quiz

1. Which of the following is the solution to the inequality $2x + 3 > 7$?
   1. $x > 2$
   2. $x < 2$
   3. $x > 5$
   4. $x < 5$
2. Solve for $x$: $-3x \leq 12$
   1. $x \leq -4$
   2. $x \geq -4$
   3. $x \leq 4$
   4. $x \geq 4$
3. Which inequality is represented by the graph with a closed circle at -1 and shading to the left?
   1. $x > -1$
   2. $x < -1$
   3. $x \geq -1$
   4. $x \leq -1$
4. Solve the compound inequality: $x + 2 < 5$ and $x - 1 > 0$
   1. $1 < x < 3$
   2. $x < 3$ or $x > 1$
   3. $x < 5$ and $x > 1$
   4. $1 < x < 5$
5. Which of the following inequalities has no solution?
   1. $x + 1 > x$
   2. $x + 1 < x$
   3. $x + 1 \geq x$
   4. $x + 1 \leq x + 2$
6. What is the solution to $4(x - 2) \leq 8$?
   1. $x \leq 4$
   2. $x \geq 4$
   3. $x \leq 6$
   4. $x \geq 6$
7. Solve for $x$: $5x - 3 > 2x + 9$
   1. $x > 2$
   2. $x < 2$
   3. $x > 4$
   4. $x < 4$