When solving an inequality by adding or subtracting the same number from both sides, what happens to the direction of the inequality symbol?

It depends on whether the number is positive or negative.

Understanding and Solving Inequalities Practice — Grade 6 math

1. To solve the inequality $x - 8 > 2$, you must add 8 to both sides. What is the resulting solution for $x$? The solution is $x >$ ___.
2. Which of the following is the correct solution to the inequality $a + 9 \leq 20$?
- A. $a \leq 11$
- B. $a \geq 11$
- C. $a \leq 29$
- D. $a \geq 29$
3. Solve the inequality $15 \geq z + 6$. If the solution is written in the form $z \leq N$, what is the value of $N$? $N = $ ___.
4. When solving an inequality by adding or subtracting the same number from both sides, what happens to the direction of the inequality symbol?
- A. It always flips.
- B. It remains the same.
- C. It changes to an equals sign.
- D. It depends on whether the number is positive or negative.
5. What is the solution to the inequality $y + 4 < -3$? The solution is $y <$ ___.
6. Solve the inequality for $x$: $5x > 45$. The solution is $x >$ ___.
7. Which of the following is the correct solution to the inequality $-4m > 24$?
- A. $m > -6$
- B. $m < -6$
- C. $m > 6$
- D. $m < 6$
8. Solve the inequality for $p$: $\frac{p}{6} \leq 3$. The solution is $p \leq$ ___.
9. When solving an inequality, what action requires you to reverse the inequality sign?
- A. Adding a negative number to both sides
- B. Subtracting a negative number from both sides
- C. Multiplying or dividing both sides by a negative number
- D. Multiplying or dividing both sides by a positive number
10. Solve the inequality for $y$: $-8y \geq -56$. The solution is $y \leq$ ___.