Algebra 1 Test Questions on Solving Two-Step Linear Inequalities

📚 Quick Study Guide

• 🔢 To solve two-step inequalities, first isolate the variable term by adding or subtracting.
• ➗ Then, multiply or divide to isolate the variable itself.
• 🔄 Remember: 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 $x < -3$.
• 💡 The solution to an inequality is a range of values. For example, $x > 4$ means any number greater than 4.
• 📈 You can represent the solution on a number line. Use an open circle for $>$ or $<$, and a closed circle for $\geq$ or $\leq$.

Practice Quiz

1. Solve the inequality: $2x + 3 < 7$

   1. $x < 2$
   2. $x > 2$
   3. $x < 5$
   4. $x > 5$

2. Solve the inequality: $-3x - 5 \geq 4$

   1. $x \leq -3$
   2. $x \geq -3$
   3. $x \leq 3$
   4. $x \geq 3$

3. Solve the inequality: $\frac{x}{2} + 1 > 5$

   1. $x > 8$
   2. $x < 8$
   3. $x > 6$
   4. $x < 6$

4. Solve the inequality: $4x - 6 \leq 2$

   1. $x \leq 2$
   2. $x \geq 2$
   3. $x \leq -2$
   4. $x \geq -2$

5. Solve the inequality: $-2x + 8 < 12$

   1. $x > -2$
   2. $x < -2$
   3. $x > 10$
   4. $x < 10$

6. Solve the inequality: $\frac{x}{-3} - 4 \geq -2$

   1. $x \leq 6$
   2. $x \geq 6$
   3. $x \leq -6$
   4. $x \geq -6$

7. Solve the inequality: $5x + 7 > 2$

   1. $x > -1$
   2. $x < -1$
   3. $x > 1$
   4. $x < 1$