Test Your Knowledge: Solving Linear Inequalities with Distribution Questions

📚 Quick Study Guide

• 🔑 Distributive Property: Remember to distribute the number outside the parentheses to each term inside: $a(b + c) = ab + ac$.
• ➕ Solving Inequalities: Solve inequalities similarly to equations, but be careful when multiplying or dividing by a negative number!
• 🔄 Flipping the Inequality Sign: If you multiply or divide by a negative number, you must flip the inequality sign. For example, if you have $-2x < 6$, dividing by -2 gives $x > -3$.
• 📈 Graphing Inequalities: Use a number line to represent the solution set. Open circles for $<$ or $>$, and closed circles for $\leq$ or $\geq$.
• ✍️ Checking Your Answer: Substitute a value from your solution set back into the original inequality to make sure it holds true.

Practice Quiz

1. What is the solution to the inequality $3(x + 2) < 9$?
   1. $x < 1$
   2. $x > 1$
   3. $x < 5$
   4. $x > 5$
2. Solve the inequality $-2(x - 1) \geq 4$.
   1. $x \leq -1$
   2. $x \geq -1$
   3. $x \leq -3$
   4. $x \geq -3$
3. What is the solution set for $4(2x - 1) > 12$?
   1. $x > 2$
   2. $x < 2$
   3. $x > -2$
   4. $x < -2$
4. Find the solution to $-(x + 3) \leq 5$.
   1. $x \geq -8$
   2. $x \leq -8$
   3. $x \geq 2$
   4. $x \leq 2$
5. Which of the following is the correct solution to $5(x - 2) < 3x$?
   1. $x < 5$
   2. $x > 5$
   3. $x < -5$
   4. $x > -5$
6. Solve: $2(3x + 1) \geq 4x + 6$
   1. $x \geq 2$
   2. $x \leq 2$
   3. $x \geq -2$
   4. $x \leq -2$
7. Determine the solution for $-3(x + 4) > 6$.
   1. $x < -6$
   2. $x > -6$
   3. $x < 2$
   4. $x > 2$