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One-Step Equation — Definition, Formula & Examples

A one-step equation is an equation that requires exactly one operation — addition, subtraction, multiplication, or division — to isolate the variable and find its value.

A one-step equation is a linear equation of the form x+a=bx + a = b, x−a=bx - a = b, ax=bax = b, or xa=b\frac{x}{a} = b, where aa and bb are known constants and xx is the unknown. The equation is solved by applying the single inverse operation that undoes the operation connecting xx to the constant.

Key Formula

x+a=b  ⟹  x=b−ax + a = b \implies x = b - a
Where:
  • xx = the unknown variable you are solving for
  • aa = a known constant added to the variable
  • bb = a known constant on the other side of the equation

How It Works

To solve a one-step equation, identify the operation that is being performed on the variable, then apply the inverse (opposite) operation to both sides. Addition undoes subtraction, and multiplication undoes division — and vice versa. Whatever you do to one side of the equation, you must do to the other side to keep it balanced. The result is the variable standing alone on one side, equal to a number on the other.

Worked Example

Problem: Solve the equation x+9=15x + 9 = 15.
Identify the operation: The variable xx has 9 added to it. The inverse of addition is subtraction.
Apply the inverse operation to both sides: Subtract 9 from both sides to isolate xx.
x+9−9=15−9x + 9 - 9 = 15 - 9
Simplify: The left side becomes xx and the right side becomes 6.
x=6x = 6
Answer: x=6x = 6

Another Example

Problem: Solve the equation 4x=284x = 28.
Identify the operation: The variable xx is being multiplied by 4. The inverse of multiplication is division.
Divide both sides by 4: Divide each side of the equation by 4 to undo the multiplication.
4x4=284\frac{4x}{4} = \frac{28}{4}
Simplify: The left side simplifies to xx and the right side simplifies to 7.
x=7x = 7
Answer: x=7x = 7

Why It Matters

One-step equations are the foundation of all equation-solving in algebra, typically introduced in 6th-grade math (standard 6.EE.B.7). Every multi-step equation you encounter later — in pre-algebra, Algebra 1, physics, or finance — ultimately breaks down into one-step operations at the end. Mastering this skill makes two-step and multi-step equations feel like natural extensions rather than new hurdles.

Common Mistakes

Mistake: Performing the operation on only one side of the equation.
Correction: An equation is a balance. Whatever you do to the left side, you must also do to the right side. For example, if you subtract 9 from the left, subtract 9 from the right as well.
Mistake: Using the same operation instead of the inverse (e.g., adding when you should subtract).
Correction: To undo an operation, apply its opposite. Addition undoes subtraction; division undoes multiplication. If the equation says x+5=12x + 5 = 12, subtract 5 — do not add 5.

Related Terms