Lesson 8-4: Describe Solutions to Linear Equations — Practice Questions

1. 1. If the equation $8x + 1 = kx + 1$ is true for all values of $x$, what is the value of $k$? The answer is ___.

2. 2. If $(p + 3)x + qy = 7x + 2y$ for all values of $x$ and $y$, what are the values of $p$ and $q$?

   • A. $p = 4, q = 2$
   • B. $p = 7, q = 2$
   • C. $p = 3, q = 2$
   • D. $p = 10, q = 0$

3. 3. Given that $(4a - 3)x + 9 = 17x + (b + 5)$ for all values of $x$, what is the value of $a$? The answer is ___.

4. 4. The equation $5x + (m - 2) = 5x + 10$ is true for all values of $x$. What is the value of $m$? The answer is ___.

5. 5. The equation $(3c)x + d = 9x - 1$ is true for all values of $x$. What is the value of $c + d$?

   • A. 2
   • B. 8
   • C. 10
   • D. 3

6. 6. Simplify the algebraic expression by distributing and combining like terms: $10 - 3(x + 2)$. The simplified expression is ___.

7. 7. Which expression is equivalent to $5(y - 3) - (y + 4)$ after simplifying?

   • A. 4y - 19
   • B. 4y - 11
   • C. 6y - 19
   • D. 5y - 11

8. 8. Simplify the expression $2(4n + 3) + 3(n - 1)$. The simplified expression is ___.

9. 9. What is the result of simplifying the expression $12 - 4(z + 2)$?

   • A. -4z + 4
   • B. -4z + 10
   • C. 8z + 16
   • D. 8z + 24

10. 10. After distributing and combining like terms in the expression $7(k - 2) - (k - 5)$, what is the simplified result? ___