When solving an inequality, the variables cancel out, leaving the statement $-2 > 0$. What does this result indicate about the solution set?

The solution is all real numbers.

An error was made in the calculation.

Solving Inequalities with Variables on Both Sides Practice — Grade 9 math

Lesson 81: Solving Inequalities with Variables on Both Sides — Practice Questions

1. When solving an inequality, the variables cancel out, leaving the statement $-2 > 0$. What does this result indicate about the solution set?
- A. The solution is all real numbers.
- B. The solution is the empty set.
- C. The solution is x = 0.
- D. An error was made in the calculation.
2. What is the solution to the inequality $9x - 4 \geq 9x + 3$?
- A. $x \geq 7$
- B. All real numbers
- C. No solution
- D. $x \leq -1$
3. Solve for $k$: $5(k + 3) < 5k + 10$. The solution set is ___.
4. Find the solution set for the inequality $4(y - 3) > 2(2y + 1)$.
- A. $y > -7$
- B. $y < 7$
- C. All real numbers
- D. No solution
5. Solve the inequality $8w - 3w + 7 \leq 5w - 1$. The solution set is ___.
6. When solving an inequality, you find that the variables cancel out, leaving the statement $-8 < 2$. What is the solution set for the original inequality?
- A. No solution
- B. All real numbers
- C. $x = -8$
- D. $x < 2$
7. To solve the inequality $9k - 4 > 9k - 15$, you subtract $9k$ from both sides. This results in the simplified numerical inequality $-4 >$ ___.
8. What is the solution to the inequality $3(a + 5) - 1 > 3a + 10$?
- A. No solution
- B. All real numbers
- C. $a > -4$
- D. $a < 14$
9. When simplifying the inequality $5(2p - 3) + 5 \le 10p + 8$, the variables cancel out, leaving the true numerical inequality ___ $\le 8$.
10. Which of the following inequalities is an identity, meaning its solution is all real numbers?
- A. $x + 5 > x + 8$
- B. $2x + 3 \le x + 3$
- C. $4x - 7 < 4x + 1$
- D. $3x > 3x$