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\( = \)
\( x \)

One-Step
Equations

Learn how to find a missing number by keeping both sides of an equation balanced.

ISEE Quantitative Reasoning

What Is an Equation?

An equation is a math sentence that says two things are equal. The equal sign \( = \) is like the middle of a balance scale: whatever is on the left must weigh the same as whatever is on the right.

\( x + 3 \)
\( 7 \)
\( = \)
 Both sides balance

The Unknown Variable

A letter like \( x \), \( n \), or \( y \) stands for a missing number we want to find. We call it the variable or unknown.

Variable
A letter that holds the place of a number, like \( x \) in \( x + 5 = 9 \).
Solving
Finding the value of the variable that makes the equation true.
Solution
The number that fits, so both sides are equal.

What Makes It One-Step?

A one-step equation needs just one move to get the variable alone. The variable has only one operation tied to it: addition, subtraction, multiplication, or division.

\( x + 6 = 10 \)
 subtract 6
\( x = 4 \)
 Just one step solves it!

The Golden Rule

To get the variable alone, undo the operation using its opposite. Whatever you do to one side, you must do to the other side too — that keeps the scale balanced.

Addition
Undo with subtraction
Subtraction
Undo with addition
Multiplication
Undo with division
Division
Undo with multiplication

Keep It Balanced

\( x + 4 = 9 \)
\( x + 4 \)
\( 9 \)
\( - 4 \)
\( - 4 \)
\( x = 5 \)

Which Operation to Undo?

Look at what is happening to the variable. Then pick the opposite operation to remove it.

Equation What's done to x Undo with
\( x + 8 = 12 \)add 8subtract 8
\( x - 5 = 3 \)subtract 5add 5
\( 6x = 18 \)multiply by 6divide by 6
\( \dfrac{x}{4} = 2 \)divide by 4multiply by 4

Steps to Solve

1
Find the operation attached to the variable.
2
Choose the opposite operation to undo it.
3
Do it to both sides of the equation.
4
Check by putting your answer back in.

Example 1: Addition

Solve \( x + 7 = 15 \).

\( x + 7 = 15 \)
\( - 7 \)
\( - 7 \)
\( x = 8 \)

Example 2: Subtraction

Solve \( n - 6 = 10 \).

\( n - 6 = 10 \)
\( + 6 \)
\( + 6 \)
\( n = 16 \)

Example 3: Multiplication

Solve \( 4x = 20 \).

\( 4x = 20 \)
\( \div 4 \)
\( \div 4 \)
\( x = 5 \)

Example 4: Division

Solve \( \dfrac{x}{3} = 6 \).

\( \frac{x}{3} = 6 \)
\( \times 3 \)
\( \times 3 \)
\( x = 18 \)

Common Mistakes

✕ One side only
Changing just one side breaks the balance. Always do the same to both sides.
✕ Same operation
Adding when you should subtract. Use the opposite operation.
✕ Skipping the check
Not plugging your answer back in to make sure both sides match.

Quick Summary

If you see Do this Example
\( x + a = b \)subtract \( a \)\( x + 2 = 9 \to x = 7 \)
\( x - a = b \)add \( a \)\( x - 2 = 9 \to x = 11 \)
\( ax = b \)divide by \( a \)\( 2x = 8 \to x = 4 \)
\( \dfrac{x}{a} = b \)multiply by \( a \)\( \dfrac{x}{2} = 8 \to x = 16 \)

Question 1 of 5

Solve for \( x \): \( \; x + 9 = 14 \)

Question 2 of 5

Solve for \( n \): \( \; n - 4 = 12 \)

Question 3 of 5

Solve for \( x \): \( \; 5x = 35 \)

Question 4 of 5

Solve for \( y \): \( \; \dfrac{y}{2} = 8 \)

Question 5 of 5

Which step solves \( \; x - 7 = 5 \)?

You've Got It!