One-Step Equations: The Complete Guide to Solving Them

Solving One-Step Equations: A Comprehensive Guide 🧮

One-step equations are the simplest type of algebraic equations to solve. They involve only one operation to isolate the variable. Let's explore how to solve them using addition, subtraction, multiplication, and division.

1. Solving with Addition ➕

If an equation involves subtracting a number from a variable, we use addition to isolate the variable.

• Example: Solve for $x$ in the equation $x - 5 = 12$.
• Solution: To isolate $x$, add 5 to both sides of the equation:

x - 5 + 5 = 12 + 5
x = 17

• Therefore, the solution is $x = 17$.

2. Solving with Subtraction ➖

If an equation involves adding a number to a variable, we use subtraction to isolate the variable.

• Example: Solve for $y$ in the equation $y + 8 = 20$.
• Solution: To isolate $y$, subtract 8 from both sides of the equation:

y + 8 - 8 = 20 - 8
y = 12

• Therefore, the solution is $y = 12$.

3. Solving with Multiplication ✖️

If an equation involves dividing a variable by a number, we use multiplication to isolate the variable.

• Example: Solve for $z$ in the equation $\frac{z}{3} = 9$.
• Solution: To isolate $z$, multiply both sides of the equation by 3:

\frac{z}{3} * 3 = 9 * 3
z = 27

• Therefore, the solution is $z = 27$.

4. Solving with Division ➗

If an equation involves multiplying a variable by a number, we use division to isolate the variable.

• Example: Solve for $a$ in the equation $4a = 32$.
• Solution: To isolate $a$, divide both sides of the equation by 4:

\frac{4a}{4} = \frac{32}{4}
a = 8

• Therefore, the solution is $a = 8$.

Summary of Steps 📝

1. Identify the operation being performed on the variable.
2. Perform the inverse operation on both sides of the equation to isolate the variable.
3. Simplify both sides to find the value of the variable.
4. Check your answer by substituting it back into the original equation.

By following these steps, you can confidently solve one-step equations involving any of the four basic operations. Practice makes perfect! 🚀