How to Solve Word Problems Involving the One-Step Equation

Word problems feel harder than straight equations, but they follow a consistent pattern. Every one-step equation word problem hides a simple equation of the form \(\color{blue}{x + a = b}\), \(\color{blue}{x – a = b}\), \(\color{blue}{\text{ ax } = b}\), or \(\color{blue}{x \div a = b}\). Once you learn to recognize the signal words and translate them into algebra, solving is straightforward. This lesson gives you a reliable 4-step method for any one-step equation word problem on the GED Math test.

What Is a One-Step Equation Word Problem?

A one-step equation word problem describes a situation where one unknown quantity is related to known quantities by a single arithmetic operation. Solving the problem requires writing and solving an equation that involves exactly one step (one operation to isolate the variable).

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Example: “Sara has some money. After spending $8, she has $15 left. How much did she start with?” translates to \(\color{blue}{x – 8 = 15}\), so \(\color{blue}{x = 23}\).

Signal Words and the Operations They Indicate

Addition signal words

sum, total, more than, added to, increased by, combined, altogether
Example: “8 more than a number is 21” → \(\color{blue}{n + 8 = 21}\)

Subtraction signal words

difference, less than, fewer, decreased by, remaining, left over, reduced by
Example: “A number decreased by 6 equals 14” → \(\color{blue}{n – 6 = 14}\)

Multiplication signal words

product, times, multiplied by, of, twice, triple, each
Example: “Three times a number is 24” → \(\color{blue}{3n = 24}\)

Division signal words

quotient, divided by, split equally, per, each share, ratio
Example: “A number divided by 5 equals 4” → \(\color{blue}{n \div 5 = 4}\)

Step-by-Step Summary

1. Read the problem and identify the unknown. Assign it a variable (usually x or n).
2. Translate the signal words into a one-step equation.
3. Solve the equation using inverse operations (opposite operation on both sides).
4. Check by substituting your answer back into the original equation and confirming both sides are equal.

Watch: Writing One-Step Equations for Word Problems (Khan Academy)

Khan Academy demonstrates the translation process from word problem to equation:

Worked Examples

Example 1: A number increased by 9 equals 17. Find the number.

Let n = the number. Equation: \(\color{blue}{n + 9 = 17}\).
Subtract 9 from both sides: \(\color{blue}{n = 17 – 9 = 8}\).
Check: \(\color{blue}{8 + 9 = 17}\) ✓  Answer: 8

Example 2: Sam had some apples. He gave away 5 and now has 12. How many did he start with?

Let x = starting apples. Equation: \(\color{blue}{x – 5 = 12}\).
Add 5 to both sides: \(\color{blue}{x = 17}\).
Check: \(\color{blue}{17 – 5 = 12}\) ✓  Answer: 17 apples

Example 3: Three times a number equals 24. What is the number?

Let n = the number. Equation: \(\color{blue}{3n = 24}\).
Divide both sides by 3: \(\color{blue}{n = 8}\).
Check: \(\color{blue}{3 \times 8 = 24}\) ✓  Answer: 8

Example 4: A book costs x dollars. You paid $20 and received $8 change. What was the price of the book?

Equation: \(\color{blue}{x + 8 = 20}\).
Subtract 8: \(\color{blue}{x = 12}\).
Check: \(\color{blue}{12 + 8 = 20}\) ✓  Answer: $12

More Practice: Solving One-Step Equations (Math with Mr. J)

Math with Mr. J shows how to isolate the variable using inverse operations:

Exercises

Write an equation for each problem and solve it.

1. A number plus 7 equals 22. Find the number.
2. Maria had some money. She spent $15 and has $30 left. How much did she start with?
3. Four times a number is 36. What is the number?
4. A number divided by 6 equals 8. Find the number.
5. A temperature dropped 11 degrees \(\color{blue}{\text{ to } -3}\)°F. What was the starting temperature?
6. There are 48 students divided equally among classrooms. If each classroom has 8 students, how many classrooms are there?

Answers

1. \(\color{blue}{n + 7 = 22}\); \(\color{blue}{n = 15}\)
2. \(\color{blue}{x – 15 = 30}\); \(\color{blue}{x = 45}\)
3. \(\color{blue}{4n = 36}\); \(\color{blue}{n = 9}\)
4. \(\color{blue}{n \div 6 = 8}\); \(\color{blue}{n = 48}\)
5. \(\color{blue}{t – 11 = -3}\); \(\color{blue}{t = 8^{\circ}F}\)
6. \(\color{blue}{48 \div c = 8}\); \(\color{blue}{c = 6}\) classrooms

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Frequently Asked Questions

How do I know which operation to use when writing the equation?

Identify the signal words in the problem. Words like “more than,” “total,” or “sum” suggest addition; “left over,” “decreased by” suggest subtraction; “times” or “each” suggest multiplication; “split equally” or “per” suggest division.

What is an inverse operation?

An inverse operation is the reverse of a given operation. Addition and subtraction are inverses; multiplication and division are inverses. To isolate the variable, apply the inverse operation to both sides of the equation.

What if I write the equation incorrectly?

Always check your answer: substitute it back into the original equation and see if both sides are equal. If they are not, re-read the problem and rethink the translation step. Most errors happen during translation, not during solving.

Related Topics

• Using Algebra Tiles to Model and Solve Equations
• Using Diagrams to Model and Solve Equations
• Using a Table to Write Down a Two Variable Equation
• Identifying Expressions and Equations
• Solving Word Problems Involving One Step Inequalities