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5-1 Solving One-Step Inequalities — Practice Questions

  1. 1. A bookshelf can hold no more than 80 pounds. It already holds 53 pounds of books. If $w$ represents the additional weight you can add, solve $53 + w \leq 80$. The maximum additional weight is ___.

  2. 2. A student needs to earn at least 120 points to pass a game level. Each round earns 8 points. Which inequality represents the number of rounds $r$ the student must play?

    • A. $8r \leq 120$
    • B. $8r \geq 120$
    • C. $r + 8 \geq 120$
    • D. $r + 8 \leq 120$
  3. 3. A school club wants to raise at least 240 dollars by selling cookies for 4 dollars each. If $c$ is the number of cookies sold, solve $4c \geq 240$. The minimum number of cookies they must sell is ___.

  4. 4. A diver descends at 15 meters per minute. To reach a depth of at least $-300$ meters, which inequality and solution correctly models the time $m$ in minutes?

    • A. $-15m \leq -300$; $m \geq 20$
    • B. $-15m \geq -300$; $m \leq 20$
    • C. $15m \leq 300$; $m \leq 20$
    • D. $-15m \leq -300$; $m \leq 20$
  5. 5. Maria has saved 47 dollars and wants to have no more than 75 dollars total before buying a gift. If $d$ represents additional dollars she can save, solve $47 + d \leq 75$. The maximum additional amount she can save is ___.

  6. 6. Solve the inequality $x + 9 \leq 20$. The solution is $x \leq$ ___.

  7. 7. Solve the inequality $4x > 28$. The solution is $x >$ ___.

  8. 8. Solve the inequality $-5x \geq 30$. The solution is $x$ ___ $-6$.

  9. 9. When solving $-3x < 18$, what is the correct solution?

    • A. $x < -6$
    • B. $x > -6$
    • C. $x < 6$
    • D. $x > 6$
  10. 10. Which operation requires you to reverse the inequality symbol when solving an inequality?

    • A. Adding 7 to both sides
    • B. Subtracting 4 from both sides
    • C. Multiplying both sides by 5
    • D. Dividing both sides by $-2$