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Chapter 2: Problem 105

What number is equal to its own double?

Short Answer

Expert verified
The number that is equal to its own double is 0.

Step by step solution

01

Formulate the equation

Let the number we are looking for be \( X \). From the problem statement, \( X \) is equal to its double. Formulate the equation as \( X = 2X \).
02

Solve the equation

Subtract \( X \) from both sides of the equation in order to isolate the variable to one side. This gives \( 0 = X \).

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Key Concepts

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

Algebraic Equations
When trying to find a specific number or variable, algebraic equations are a fundamental tool. An equation puts forth a statement that two expressions are equivalent. The exercise here prompts the identification of a number that is equal to twice its own value. This scenario is represented as the equation \( X = 2X \).

The equation symbolizes a balance and the challenge lies in finding the value of \( X \) that maintains this balance. Subsequently, we found that indeed, no number can satisfy this condition except for 0, which is deduced by the subtraction of \( X \) from both sides leading to the solution \( 0 = X \).
Problem-Solving in Algebra
Addressing algebraic problems requires a systematic approach. The first step is always to understand the problem and then translate it into a mathematical expression or equation. In our example, the translation was direct: a number (\( X \)) is equal to its own double (\( 2X \)).

After formulating the equation, the next step is manipulation to isolate the variable of interest; here, the subtraction of \( X \) from both sides was crucial. This standard method of problem-solving in algebra, moving terms to simplify the equation, paved the way to the surprising yet accurate conclusion that our number is 0.
Basic Algebra Concepts
Getting to grips with the basics in algebra paves the way for solving more complex mathematical problems. The principle exercises often involve variables, constants, and the operations that connect them. To solve for variables, algebra teaches us to perform the same operation on both sides of an equation to maintain equality.

In our textbook exercise, subtraction was the operation used to simplify and solve the equation. What this teaches is the concept of equivalent operations and understanding the properties of zero in algebra. Essentially, when a variable is subtracted from itself, it results in zero, which is a crucial starting point for many algebraic solutions.

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Most popular questions from this chapter

Solve. Find the tax paid on an item that was priced at \(\$ 37.10\) and cost \(\$ 39.32 .\)

The power \(P\) lost when an electric current \(I\) passes through a resistance \(R\) is given by the formula \(P=I^{2} R\) Solve for \(R .\) If \(P\) is 2,700 watts and \(I\) is 14 amperes, calculate \(R\) to the nearest hundredth of an ohm.

Solve each inequality and graph the solution on the number line. $$-12 \leq \frac{x}{3} < 0$$

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