Key takeaway: A one-step equation is an equation that needs just one inverse operation applied to both sides to isolate the variable, as in x + 17.5 = 42 or n/4 = 9.5.
Grade 66.EE.B.7Expressions and Equations
Definition of One-Step Equation
A one-step equation has a variable that is touched by only one operation: something was added to it, subtracted from it, multiplied by it, or divided into it. To solve it, undo that operation.
The rule is to do the same thing to both sides. In \(x + 17.5 = 42\), the 17.5 was added, so subtract 17.5 from both sides. The variable ends up alone, and the other side shows its value. Always finish by substituting the answer back to confirm that the original statement is true.
Formula and notation
The four basic forms and their solutions are
\[x + a = b \ \text{gives}\ x = b – a \qquad x – a = b \ \text{gives}\ x = b + a\]\[ax = b \ \text{gives}\ x = \frac{b}{a} \qquad \frac{x}{a} = b \ \text{gives}\ x = ab\]
In the last two, \(a \neq 0\).
Key facts
- Every one-step equation is solved with the partner of its single operation.
- Whatever you do to one side must be done to the other side too.
- Check by substituting the solution into the original equation.
- A one-step equation with decimals or fractions follows the same rules as one with whole numbers.
One-Step Equation example
Marcus’s savings jar had some money in it. After he added \$17.50, the jar held \$42. Solve \(x + 17.5 = 42\) for the amount he started with, and then solve \(\frac{n}{4} = 9.5\).
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Subtract 17.5 from both sides: \(x = 42 – 17.5 = 24.5\).
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Check: \(24.5 + 17.5 = 42\). It works.
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For \(\frac{n}{4} = 9.5\), multiply both sides by 4: \(n = 9.5 \times 4 = 38\).
Marcus started with \$24.50, and \(n = \) 38.
Common mistake
Watch out
Zoe solves \(\frac{n}{4} = 9.5\) by subtracting 4: \(n = 5.5\).
Why it is wrong
The variable is being divided by 4, so the undoing operation is multiplication, not subtraction. \(n = 9.5 \times 4 = 38\). Check: \(38 : 4 = 9.5\), while \(5.5 : 4 \neq 9.5\).
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Expressions and Equations