Algebra 1 Quiz: Solving Equations with Variables on Both Sides

📚 Quick Study Guide

• 🔢Isolate the Variable: Your main goal is to get all the terms with the variable (like $x$) on one side of the equation and all the constant terms (numbers) on the other side.
• ➕Addition/Subtraction: Use addition or subtraction to move terms across the equals sign. Remember to do the same operation to both sides of the equation to keep it balanced! If you have $3x + 5 = x - 1$, subtract $x$ from both sides to get $2x + 5 = -1$.
• ➗Multiplication/Division: Use multiplication or division to isolate the variable completely. If you have $2x = -6$, divide both sides by 2 to get $x = -3$.
• 💡Simplify: Combine like terms on each side of the equation before isolating the variable.
• ✅Check Your Answer: Plug your solution back into the original equation to make sure it's correct. If both sides of the equation are equal, your solution is valid!

🧪 Practice Quiz

1. What is the solution to the equation $5x - 3 = 2x + 6$?
   1. A) $x = 1$
   2. B) $x = 3$
   3. C) $x = -3$
   4. D) $x = 0$
2. Solve for $y$: $7y + 2 = 4y - 7$
   1. A) $y = -3$
   2. B) $y = 3$
   3. C) $y = 1$
   4. D) $y = -1$
3. What is the value of $z$ in the equation $3z - 5 = z + 1$?
   1. A) $z = -3$
   2. B) $z = 3$
   3. C) $z = 1$
   4. D) $z = -1$
4. Find the solution for $4a + 8 = a - 1$
   1. A) $a = 3$
   2. B) $a = -3$
   3. C) $a = -1$
   4. D) $a = 1$
5. Solve: $6b - 4 = 2b + 8$
   1. A) $b = -3$
   2. B) $b = 3$
   3. C) $b = 1$
   4. D) $b = 4$
6. Determine the value of $x$: $9x + 3 = 6x - 6$
   1. A) $x = -3$
   2. B) $x = 3$
   3. C) $x = 1$
   4. D) $x = -1$
7. What is the solution to the equation $2w - 7 = -3w + 3$?
   1. A) $w = 1$
   2. B) $w = 2$
   3. C) $w = 3$
   4. D) $w = 4$