Introduction

One-step equations are the simplest type of algebraic equations.
They involve only one operation, such as adding or subtracting a number.
Your goal is to “undo” that operation to find the value of the unknown.

This article assumes you already understand basic arithmetic (adding, subtracting, and working with negative numbers).

What Is an Equation?

• An equation is a mathematical statement that two things are equal.
• It always contains an equals sign $=$.
• Example:
  • $x + 5 = 12$
  • $7 = y - 3$

In these examples, $x$ and $y$ are unknowns—numbers we want to find.

Inverse Operations

To solve an equation, we use inverse operations—operations that undo each other:

• Addition ↔ Subtraction
• Subtraction ↔ Addition

Examples:

• The inverse of $+7$ is $-7$
• The inverse of $-4$ is $+4$

Using inverse operations helps us isolate the unknown.

Solving One-Step Addition Equations

When the equation has addition, we undo it with subtraction.

General idea:

• If $x + a = b$, then subtract $a$ from both sides: $$x = b - a$$

Example:

• Solve $x + 6 = 10$
  • Subtract $6$ from both sides
  • $x = 10 - 6 = 4$

Key points:

• Always perform the same operation on both sides.
• The goal is to get the unknown by itself.

Solving One-Step Subtraction Equations

When the equation has subtraction, we undo it with addition.

General idea:

• If $x - a = b$, then add $a$ to both sides: $$x = b + a$$

Example:

• Solve $x - 3 = 8$
  • Add $3$ to both sides
  • $x = 8 + 3 = 11$

Key points:

• Keep track of negative numbers carefully.
• Adding a number can make the equation simpler.

Checking Your Solution

After solving, plug your answer back into the original equation.

Example:

• Original: $x + 4 = 9$
• Solution: $x = 5$
• Check: $5 + 4 = 9$ ✔️

If both sides match, your solution is correct.

Common Mistakes to Avoid

• Forgetting to apply the operation to both sides.
• Mixing up signs (especially with negative numbers).
• Stopping before isolating the unknown.

Tips:

• Write each step clearly.
• Use inverse operations consistently.
• Double-check with substitution.

Calculator

Exercises

1. Solve the equation: $x + 7 = 15$

   Solution

   $x + 7 = 15$
   Subtract $7$ from both sides: $$x = 15 - 7 = 8$$
2. Solve the equation: $y - 4 = 9$

   Solution

   $y - 4 = 9$
   Add $4$ to both sides: $$y = 9 + 4 = 13$$
3. Solve for $x$: $x + 12 = 3$

   Solution

   $x + 12 = 3$
   Subtract $12$: $$x = 3 - 12 = -9$$
4. Solve for $m$: $m - 10 = -2$

   Solution

   $m - 10 = -2$
   Add $10$: $$m = -2 + 10 = 8$$
5. Solve the equation: $k - 6 = -12$

   Solution

   $k - 6 = -12$
   Add $6$: $$k = -12 + 6 = -6$$
6. Solve for $x$: $x + (-5) = 8$

   Solution

   $x + (-5) = 8$
   Add $5$: $$x = 8 + 5 = 13$$
7. Solve the equation: $p - (-3) = 7$

   Solution

   $p - (-3) = 7$
   Subtracting a negative is adding a positive: $$p = 7 + 3 = 10$$
8. Solve for $t$: $t + 9 = -4$

   Solution

   $t + 9 = -4$
   Subtract $9$: $$t = -4 - 9 = -13$$