Picture this: You’re sitting in your math class, and your teacher writes a word problem on the board. “If 10 is added to four times a certain number…” Your mind starts racing. How do you even begin to solve this? Don’t worry you’re not alone. This type of algebraic expression confuses thousands of students every day, but once you understand the pattern, it becomes surprisingly simple.
Learning to translate words into mathematical expressions is one of the most important skills in algebra. It helps you solve real-world problems, from calculating discounts during shopping to understanding patterns in science experiments. This guide will break down everything you need to know about this concept in the simplest way possible.
What Does “If 10 Be Added to Four Times a Number” Mean?
Let’s decode this phrase word by word.
“A number” means any unknown value. In algebra, we represent this with a variable like x, y, or n.
“Four times a number” means multiplying that unknown number by 4. If the number is x, then four times that number is 4x.
“10 be added to” means we’re adding 10 to whatever we calculated before.
So the complete expression becomes: 4x + 10
Think of it like ordering pizza. If one pizza costs x rupees, then four pizzas cost 4x rupees. If you also pay a ₹10 delivery charge, your total becomes 4x + 10.
Breaking Down the Expression Step by Step
Understanding the order of operations helps you translate word problems correctly.
Step 1: Identify the Unknown
The phrase says “a number”—this is your variable. Let’s call it x.
Step 2: Handle “Four Times”
“Four times a number” means multiplication: 4 × x = 4x
Step 3: Add the Constant
“10 be added” means we’re adding 10 to what we already have: 4x + 10
Visual Breakdown Table
| Phrase | Mathematical Operation | Result |
|---|---|---|
| A number | Unknown variable | x |
| Four times a number | Multiplication | 4x |
| 10 be added to | Addition | 4x + 10 |
Writing the Algebraic Expression
The standard algebraic expression for “if 10 be added to four times a number” is:
4x + 10
This can also be written as:
- 10 + 4x (due to commutative property of addition)
- 4(x) + 10
- 2(2x) + 10 (factored differently)
All these forms are mathematically correct, but 4x + 10 is the most common and preferred format.
Solving Complete Equations
Usually, this expression appears in complete equations where you need to find the value of x.
Example 1: Basic Equation
Problem: If 10 is added to four times a number, the result is 50. Find the number.
Solution:
- Expression: 4x + 10 = 50
- Subtract 10 from both sides: 4x = 40
- Divide both sides by 4: x = 10
- Answer: The number is 10
Example 2: Exam-Style Question
Problem: If 10 is added to four times a number, the answer equals 10 times the power of 4.
Solution:
- Four to the power of 1 is 4, so 10 times 4 = 40
- Expression: 4x + 10 = 40
- Subtract 10: 4x = 30
- Divide by 4: x = 7.5
- Answer: The number is 7.5
Example 3: Negative Result
Problem: If 10 is added to four times a number and the result is -2, what is the number?
Solution:
- Expression: 4x + 10 = -2
- Subtract 10: 4x = -12
- Divide by 4: x = -3
- Answer: The number is -3
Real-Life Classroom Examples
Scenario 1: Test Scores
Priya’s final exam score is calculated by taking four times her assignment marks and adding 10 bonus points. If her final score is 90, what were her assignment marks?
- 4x + 10 = 90
- 4x = 80
- x = 20 marks
Scenario 2: Money Calculation
Rahul has some money. His father gives him four times what he has, plus ₹10 extra. Now he has ₹110. How much money did Rahul originally have?
- 4x + 10 = 110
- 4x = 100
- x = ₹25
Scenario 3: Age Problem
A mother’s age is 10 years more than four times her daughter’s age. If the mother is 46, how old is the daughter?
- 4x + 10 = 46
- 4x = 36
- x = 9 years old
Common Mistakes Students Make
1. Wrong Order of Operations
Incorrect: 10 × 4 + x = 40 + x Correct: 4 × x + 10 = 4x + 10
Students often multiply 10 and 4 first instead of applying “four times” to the variable.
2. Confusing “Added To” with “Added From”
Incorrect: 10 – 4x (subtraction) Correct: 4x + 10 (addition)
The phrase “added to” always means addition, not subtraction.
3. Forgetting to Multiply First
Incorrect: (4 + x) + 10 Correct: 4x + 10
“Four times a number” means multiply first, not add four to the number.
4. Dividing Incorrectly
When solving 4x + 10 = 50, students sometimes divide 50 by 4 directly without subtracting 10 first.
Wrong approach: x = 50 ÷ 4 = 12.5
Right approach: Subtract 10 first, then divide by 4 to get x = 10
Quick Tips and Memory Tricks
The PEMDAS Memory Trick
Remember: Please Excuse My Dear Aunt Sally
- Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
- “Four times” comes before “added to” because multiplication comes before addition
Translation Chart
- “Times” = Multiplication (×)
- “Added to” = Addition (+)
- “More than” = Addition (+)
- “Less than” = Subtraction (−)
- “Is/Equals/Results in” = Equals sign (=)
The Left-to-Right Reading Rule
Read the problem left to right, but write the expression in the correct mathematical order:
- Read: “10 be added to four times a number”
- Write: 4x + 10 (multiply first, then add)
Practice Makes Perfect
Solve 5 similar problems daily for one week. By day 7, you’ll translate these expressions automatically without thinking.
Related Concepts You Should Know
Similar Expressions to Practice
“10 times as much as 4”
- Expression: 10 × 4 = 40
- This is a straightforward multiplication
“What is 10 times the power of 4?”
- Expression: 10 × 4¹ = 40
- Or 10 × 4² = 160 (if power is 2)
“What happens when you add 10 to a number?”
- Expression: x + 10
- This is simple addition without multiplication
“How do you divide 10 into 4?”
- Expression: 10 ÷ 4 = 2.5
- This involves division, not addition or multiplication
The Bridge to Advanced Topics
Understanding “if 10 be added to four times a number” prepares you for:
- Linear equations
- Word problem solving
- Function notation
- Algebraic modeling
- Real-world applications in physics and economics
Frequently Asked Questions about if 10 be added to four times a number
Q. What is the algebraic expression for “if 10 be added to four times a number”?
The expression is 4x + 10, where x represents the unknown number. First multiply the number by 4, then add 10 to that result.
Q. How do you solve if 10 added to four times a number equals 50?
Set up the equation 4x + 10 = 50. Subtract 10 from both sides to get 4x = 40, then divide by 4. The answer is x = 10.
Q. What does “four times a number” mean in mathematics?
It means multiplying the unknown number by 4. If the number is represented by x, then four times the number is written as 4x or 4 × x.
Q. Is 4x + 10 the same as 10 + 4x?
Yes, both expressions are mathematically equivalent due to the commutative property of addition. However, 4x + 10 is the standard preferred format in algebra.
Q. What are common mistakes when solving these problems?
Students often multiply 10 and 4 first instead of multiplying 4 by the variable. Another mistake is forgetting to subtract before dividing when solving equations.
Q. How is this different from “10 times the power of 4”?
“10 times the power of 4” means 10 × 4¹ = 40, which is a single calculation. “If 10 be added to four times a number” involves an unknown variable: 4x + 10.
Q. Can this expression have a negative answer?
Yes, if solving an equation like 4x + 10 = -10, you would get 4x = -20, so x = -5. Negative numbers are valid solutions in algebra.
Q. Why is understanding this concept important for students?
This skill is fundamental for translating word problems into mathematical equations, which is essential for solving real-world problems in physics, chemistry, economics, and everyday calculations.
Conclusion
Mastering “if 10 be added to four times a number” is more than just learning a formula it’s about developing your ability to think mathematically and solve real-world problems. The expression 4x + 10 appears everywhere, from calculating bills to understanding scientific formulas.
Remember the key steps: identify your variable, apply multiplication before addition, and always work through problems methodically. With practice, what once seemed confusing becomes second nature.
Every mathematician, engineer, and scientist started exactly where you are now learning to translate words into numbers. Keep practicing, stay curious, and don’t be afraid to make mistakes. Each problem you solve builds your confidence and sharpens your problem-solving skills.