Lesson 1: The Basics — Practice Questions

1. 1. Solve the inequality for $m$: $m + 5 > 12$. The solution is $m >$ ___.

2. 2. If you are solving the inequality $p - 11 \leq -3$, which property should you use to find the solution?

   • A. Addition Property of Inequality
   • B. Subtraction Property of Inequality
   • C. Multiplication Property of Inequality
   • D. Division Property of Inequality

3. 3. Solve for $y$ in the inequality $y - 6 > -2$. The solution is $y >$ ___.

4. 4. Which inequality is equivalent to the solution for $k + 8 \geq 19$?

   • A. $k \geq 11$
   • B. $k \leq 11$
   • C. $k \geq 27$
   • D. $k \leq 27$

5. 5. Solve for $x$: $x + \frac{1}{2} < 4$. The solution is $x <$ ___. (Enter as a fraction)

6. 6. Given that $7 > 4$ and both numbers are positive, which of the following inequalities is true based on the exponentiation rule?

   • A. $7^2 < 4^2$
   • B. $7^2 > 4^2$
   • C. $7^2 = 4^2$
   • D. The relationship cannot be determined.

7. 7. Given the inequality $144 > 81 > 0$, taking the square root of both sides results in the new inequality $12 >$ ___.

8. 8. Given the inequality $10 > 9 > 0$, which statement correctly applies the property for taking roots?

   • A. $\sqrt{10} < \sqrt{9}$
   • B. $\sqrt{10} > \sqrt{9}$
   • C. $\sqrt{10} = \sqrt{9}$
   • D. The property cannot be applied.

9. 9. Given that $27 > 8 > 0$, applying the exponentiation rule with a power of $1/3$ gives the inequality $3 >$ ___.

10. 10. The rule 'If $a > b$, then $a^n > b^n$ for a positive power $n$' is only guaranteed to be true under which condition?

    • A. $a$ and $b$ are integers
    • B. $n$ is an integer
    • C. $a > b > 0$
    • D. $a > 0$ and $b < 0$