Examples of One-Step Linear Equations for 7th Graders

📚 Quick Study Guide

• 🔢 A linear equation is an equation where the highest power of the variable is 1. For example, $x + 5 = 10$ is a linear equation.
• ➕ To solve a one-step linear equation, you need to isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, or division).
• ➖ The goal is to get the variable by itself (e.g., $x = ext{some number}$).
• ➗ Remember, whatever operation you perform on one side of the equation, you must perform on the other side to maintain equality.
• 💡 If the equation involves addition, subtract from both sides. If it involves subtraction, add to both sides. If it involves multiplication, divide both sides. If it involves division, multiply both sides.
• ✍️ Example: Solve $x - 3 = 7$. Add 3 to both sides: $x - 3 + 3 = 7 + 3$, which simplifies to $x = 10$.

Practice Quiz

1. What is the solution to the equation $x + 5 = 12$?
   1. $x = 5$
   2. $x = 7$
   3. $x = 17$
   4. $x = 60$
2. Solve for $y$ in the equation $y - 8 = 3$.
   1. $y = 5$
   2. $y = 11$
   3. $y = -5$
   4. $y = 24$
3. What value of $z$ satisfies the equation $3z = 21$?
   1. $z = 3$
   2. $z = 63$
   3. $z = 7$
   4. $z = 18$
4. Find the solution to the equation $\frac{a}{4} = 5$.
   1. $a = 1$
   2. $a = 9$
   3. $a = \frac{5}{4}$
   4. $a = 20$
5. If $b + 2.5 = 6$, what is the value of $b$?
   1. $b = 8.5$
   2. $b = 3.5$
   3. $b = 15$
   4. $b = 2.4$
6. Solve for $c$: $c - 1.2 = 4.8$
   1. $c = 3.6$
   2. $c = 6$
   3. $c = 4$
   4. $c = 5.6$
7. What is the solution to the equation $5x = 35$?
   1. $x = 7$
   2. $x = 30$
   3. $x = 40$
   4. $x = 175$