Solving Equations: Variables on Both Sides - Examples and Solutions

📚 Quick Study Guide

• ⚖️ The Goal: Isolate the variable on one side of the equation.
• ➕ Addition/Subtraction Property: Add or subtract the same value from both sides to move terms.
• ➗ Multiplication/Division Property: Multiply or divide both sides by the same non-zero value to isolate the variable.
• 🔄 Combining Like Terms: Simplify each side of the equation before isolating the variable.
• ✔️ Checking Your Solution: Substitute your solution back into the original equation to verify it's correct.
• 📝 Example: Solve $3x + 5 = x - 1$:
  • Subtract $x$ from both sides: $2x + 5 = -1$
  • Subtract $5$ from both sides: $2x = -6$
  • Divide both sides by $2$: $x = -3$

Practice Quiz

1. What is the first step in solving the equation $5x - 3 = 2x + 9$?
   1. Combine the $x$ terms.
   2. Add 3 to both sides.
   3. Subtract 9 from both sides.
   4. Divide both sides by 5.
2. Solve for $x$: $4x + 7 = x - 5$
   1. $x = -4$
   2. $x = -12/5$
   3. $x = -2$
   4. $x = -3$
3. Solve for $y$: $7y - 2 = 3y + 6$
   1. $y = 1$
   2. $y = 2$
   3. $y = 3$
   4. $y = 4$
4. Solve: $2(a + 3) = 5a - 9$
   1. $a = 5$
   2. $a = 1$
   3. $a = 7$
   4. $a = 3$
5. What is the value of $z$ in the equation $6z + 4 = 2z - 8$?
   1. $z = -1$
   2. $z = -2$
   3. $z = -3$
   4. $z = -4$
6. Find the solution to the equation: $8w - 10 = 3w + 5$
   1. $w = 1$
   2. $w = 2$
   3. $w = 3$
   4. $w = 4$
7. Solve for $x$: $-3x + 7 = 5x - 1$
   1. $x = 0$
   2. $x = 1$
   3. $x = 2$
   4. $x = 3$