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Chapter 3: Problem 42

A certain number added to 14 is 25 . Find the number.

Short Answer

Expert verified
The number is 11.

Step by step solution

01

Identify known values

First, we start by identifying the known values from the problem. We know that a certain number, which we'll call \( x \), is added to 14. This gives a total of 25.
02

Write the equation

Using the known values, write an equation to represent the situation: \( x + 14 = 25 \)
03

Solve for the unknown

To isolate \( x \), subtract 14 from both sides of the equation:\( x + 14 - 14 = 25 - 14 \) This simplifies to:\( x = 11 \)
04

Verify the solution

Check your solution by plugging \( x = 11 \) back into the original equation:\( 11 + 14 = 25 \). Since the calculation is correct, the solution \( x = 11 \) is verified.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solving Equations
Solving equations in algebra involves finding the value of the unknown variable that makes the equation true. An equation is like a balance scale. What you do to one side, you must do to the other to keep it balanced. In the exercise, the equation was set up as \( x + 14 = 25 \), where our task was to find the value of \( x \).
To solve it, we performed the same operation on both sides鈥攖he act of subtracting 14 from both sides of the equation鈥攖o isolate \( x \).
This made the equation simpler, leading us to the solution \( x = 11 \).
  • Start by identifying known values and what is needed.
  • Perform operations equally on both sides.
  • Check your solution to ensure accuracy.
Algebraic Expressions
Algebraic expressions are a fundamental component of algebra, comprising numbers, variables, and operations. In our problem, the expression \( x + 14 \) represents an unknown number \( x \) that we add to 14. Expressions do not have an equals sign and are used to describe a part of an equation or a more complex algebraic statement.
Learning to simplify expressions is crucial. In our scenario, understanding the expression \( x + 14 \) was key to forming the correct equation and subsequently solving for \( x \).
  • Expressions comprise variables like \( x \) and constants like 14.
  • No equals sign to indicate a complete equation.
  • Understanding expressions helps in setting and solving equations.
Basic Arithmetic Operations
Basic arithmetic operations lay the groundwork for algebra and involve addition, subtraction, multiplication, and division. They enable us to manipulate numbers and expressions in equations. In our exercise, addition and subtraction were used. We began with the expression \( x + 14 \) and needed to solve for \( x \) by employing the inverse operation of addition, which is subtraction.
By subtracting 14 from both sides of the equation \( x + 14 = 25 \), we effectively simplified the problem to find that \( x = 11 \).
  • Addition helps combine numbers.
  • Subtraction helps isolate terms in solving equations.
  • These operations are fundamental tools in elementary algebra.

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