Real-world examples of solving equations with decimals

📚 Quick Study Guide

• 🔢 To solve equations with decimals, the primary goal is to isolate the variable on one side of the equation.
• ➗ Sometimes, you can directly add, subtract, multiply, or divide both sides of the equation to isolate the variable.
• ✖️ If you prefer working with whole numbers, you can multiply both sides of the equation by a power of 10 (10, 100, 1000, etc.) to eliminate the decimals. Ensure you multiply every term on both sides.
• ⚖️ Remember to perform the same operations on both sides of the equation to maintain balance.
• ✅ After finding a solution, substitute it back into the original equation to verify its correctness.
• 💰 A practical application involves calculating costs, discounts, or commissions. For example, calculating the sale price of an item with a percentage discount.
• 💡 In science, these equations can appear when calculating concentrations or reaction rates.

🧪 Practice Quiz

1. What is the value of $x$ in the equation $0.2x + 1.5 = 2.5$?
   1. 0.5
   2. 5
   3. 20
   4. 2
2. Solve for $y$: $3.5y - 2.1 = 1.4$
   1. 0.1
   2. 1
   3. 10
   4. 0.5
3. A store is offering a 15% discount on an item priced at $25.50. What is the sale price of the item after the discount?
   1. $21.68
   2. $3.83
   3. $29.33
   4. $21.67
4. Find the value of $z$: $0.05z = 3.25$
   1. 6.5
   2. 65
   3. 0.65
   4. 650
5. If $2.5a + 7.5 = 15$, what is the value of $a$?
   1. 2
   2. 3
   3. 4
   4. 5
6. Solve: $1.2b - 4.8 = 0$
   1. 4
   2. 0.4
   3. 6
   4. -4
7. What is the solution to $5.5 = 1.1c$?
   1. 6.05
   2. 5
   3. 4.4
   4. 0.2