One-Step Equation
In short: A one-step equation can be solved with a single undo move on both sides, like subtracting 9 from each side of x + 9 = 31 to find that x is 22.
6th GradeAlgebra6.EE.B.7
What is One-Step Equation?
A one-step equation hides the variable behind a single operation: added to, subtracted from, multiplied by or divided by a number. One matching undo move frees the variable.
Precisely, the forms are \(x + a = b\), \(x – a = b\), \(ax = b\) and \(\frac{x}{a} = b\) with \(a \neq 0\). Whatever you do to one side you must also do to the other, so the equation stays true and its solution does not change.
How to spot it
- An unknown is tied to just one number by one operation, such as \(5y = 65\).
- A story hands you a total and a single known piece, and the missing piece is the unknown.
- A balance-scale picture needs one weight removed, or a load split evenly into groups.
- Only one operation sign sits between the letter and the number on that side.
The method
- Name the operation attached to the letter: plus, minus, times or divide.
- Apply the opposite operation to the left side and to the right side, using the same number on each.
- Simplify both sides until the letter stands alone with a number beside it.
- Plug the number back into the starting line; both sides should then read the same.
One-Step Equation: solved example
Problem
A school raised $432 at a bake sale. That is 9 times what the chess club raised. Solve \(9c = 432\) to find the chess club’s amount.
Solution
The variable is multiplied by 9, so divide both sides by 9: \(\frac{9c}{9} = \frac{432}{9}\).
That gives \(c = 48\). Check: \(9 \cdot 48 = 432\). The chess club raised $48.
Try it
Question 1
Solve \(y – 17 = 26\).
Show the answer
Add 17 to both sides: \(y = 43\).
Question 2
Solve \(\frac{k}{4} = 2.5\).
Show the answer
Multiply both sides by 4: \(k = 10\).
One-Step Equation vs. Inverse Operations
The equation is the problem you are solving. The inverse operation is the move you pick to solve it: subtract to undo adding, divide to undo multiplying. A one-step equation needs exactly one such move.
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Whole dictionary: A–Z · 6th Grade · Algebra