What is an Equation? Definition and Examples for Algebra 1

📚 Quick Study Guide

🔢 Definition: An equation is a mathematical statement that two expressions are equal. It contains an equals sign (=). ⚖️ Key Concept: The goal is usually to find the value of a variable (like $x$) that makes the equation true. ➕ Basic Operations: Use addition, subtraction, multiplication, and division to isolate the variable. Remember, what you do to one side, you MUST do to the other! 💡 Solving Equations:
✅ Simplify each side of the equation. ✅ Use inverse operations to isolate the variable. ✅ Check your solution by plugging it back into the original equation.
📝 Example: $x + 5 = 10$. To solve for $x$, subtract 5 from both sides: $x + 5 - 5 = 10 - 5$, which simplifies to $x = 5$.

Practice Quiz

1. Which of the following is an equation?
   1. $2x + 3$
   2. $y - 7$
   3. $4 + 5 = 9$
   4. $a > 2$
2. Solve for $x$: $x - 3 = 7$
   1. $x = 3$
   2. $x = 4$
   3. $x = 10$
   4. $x = 21$
3. Solve for $y$: $2y = 12$
   1. $y = 2$
   2. $y = 6$
   3. $y = 10$
   4. $y = 24$
4. Solve for $a$: $a + 4 = 9$
   1. $a = 36$
   2. $a = 13$
   3. $a = 5$
   4. $a = 4$
5. Solve for $b$: $\frac{b}{3} = 5$
   1. $b = \frac{5}{3}$
   2. $b = 2$
   3. $b = 15$
   4. $b = 8$
6. Solve for $z$: $z - 2 = 11$
   1. $z = 9$
   2. $z = 13$
   3. $z = 22$
   4. $z = 15$
7. Which operation would you use to isolate $x$ in the equation $x + 8 = 15$?
   1. Addition
   2. Subtraction
   3. Multiplication
   4. Division