Lesson 2: Solving Equations of the Form px+q=r and p(x+q)=r and Problems That Lead to Those Equations — Practice Questions

1. 1. Solve for $x$ in the following equation: $3x + 7 = 28$. The value of $x$ is ___.

2. 2. Maria bought 4 identical notebooks and a pen for 3 dollars. The total cost was 15 dollars. The price of one notebook is ___ dollars.

3. 3. Find the value of $a$ that makes the equation true: $6a + 2 = 38$. The value of $a$ is ___.

4. 4. Which value of $z$ is the solution to the equation $2z + 9 = 23$?

   • A. 5
   • B. 7
   • C. 12
   • D. 16

5. 5. A gym membership costs 15 dollars per month plus a one-time 25 dollar fee. If a member paid 100 dollars total, how many months was the membership for? ___ months.

6. 6. Solve the equation for the value of $x$: $5(x+2) = 35$. The value of $x$ is ___.

7. 7. What is the resulting equation after the first step of dividing both sides to solve $8(z+1)=40$?

   • A. $z+1 = 5$
   • B. $8z+8 = 40$
   • C. $z+8 = 40$
   • D. $z = 4$

8. 8. Solve the equation for the value of $y$: $6(y-4) = 18$. The value of $y$ is ___.

9. 9. Solve the equation for the value of $k$: $-2(k+5) = -10$. The value of $k$ is ___.

10. 10. When solving $2(x+5)=14$, how does the solution from dividing first compare to the solution from distributing first?

    • A. The solution from dividing first is smaller.
    • B. The solution from distributing first is smaller.
    • C. Both methods yield the same solution.
    • D. The methods cannot be compared.