Test questions for Grade 7 one-step inequalities with negative multipliers

📚 Quick Study Guide

• 🔢 When solving one-step inequalities with negative multipliers, remember that multiplying or dividing both sides by a negative number requires you to flip the inequality sign.
• 🧮 For example, if you have $-2x > 6$, dividing both sides by $-2$ gives $x < -3$. Notice the `>` sign changed to `<`.
• 💡 This is because multiplying or dividing by a negative number reverses the order of numbers on the number line.
• 📝 Key steps include:
  1. Isolate the variable term.
  2. Divide or multiply both sides by the coefficient of the variable.
  3. Remember to flip the inequality sign if the coefficient is negative.
• 📊 Here's a quick reference:

  Original Inequality	Operation	New Inequality
  $ax > b$ (where $a < 0$)	Divide by $a$	$x < \frac{b}{a}$
  $ax < b$ (where $a < 0$)	Divide by $a$	$x > \frac{b}{a}$
  $\frac{x}{a} > b$ (where $a < 0$)	Multiply by $a$	$x < ab$
  $\frac{x}{a} < b$ (where $a < 0$)	Multiply by $a$	$x > ab$

🧪 Practice Quiz

1. What is the solution to the inequality $-3x \le 12$?
   1. $x \le -4$
   2. $x \ge -4$
   3. $x \le 4$
   4. $x \ge 4$
2. Solve for $x$: $-2x > -8$
   1. $x > 4$
   2. $x < 4$
   3. $x > -4$
   4. $x < -4$
3. What is the solution set for $-\frac{x}{4} < 2$?
   1. $x < -8$
   2. $x > -8$
   3. $x < 8$
   4. $x > 8$
4. Find the solution to $-5x \ge -25$
   1. $x \ge 5$
   2. $x \le 5$
   3. $x \ge -5$
   4. $x \le -5$
5. Solve: $-x > 7$
   1. $x > -7$
   2. $x < -7$
   3. $x > 7$
   4. $x < 7$
6. What values of $x$ satisfy $-6x < 18$?
   1. $x < -3$
   2. $x > -3$
   3. $x < 3$
   4. $x > 3$
7. Solve the inequality: $-\frac{x}{3} \ge -1$
   1. $x \ge 3$
   2. $x \le 3$
   3. $x \ge -3$
   4. $x \le -3$