Question

Which of the following is an equation ?

• A. \(x + 1\)
• B. \(x - 1 = 0\)
• C. \(x - 1\)
• D. \(x + 1 \gt 0\)

Hint:

An equation MUST contain the equality sign (\(=\)).
If there is no "\(=\)", it is either an expression (no relation symbol) or an inequality (contains order symbols).
This single check immediately identifies \(x - 1 = 0\) as the correct answer.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question is from Basic Algebra, focusing on the terminology and definitions of mathematical statements.
We need to distinguish between expressions, equations, and inequalities.

Step 2: Key Formula or Approach:
1. An algebraic expression consists of variables, numbers, and operations, but lacks a relation symbol (e.g., \(x + 1\)).
2. An equation is a mathematical statement asserting the equality of two expressions, indicated by an equal sign (\(=\)).
3. An inequality expresses a relationship of order, indicated by symbols like \(\gt \), \(\lt \), \(\ge\), or \(\le\) (e.g., \(x + 1 \gt 0\)).

Step 3: Detailed Explanation:
Let us evaluate each of the given options:
Option (A): \(x + 1\)
This is a polynomial of degree one. It is an expression, not an equation, because it lacks an equality relation.
Option (B): \(x - 1 = 0\)
This statement equates the linear expression \(x - 1\) to the constant \(0\). The presence of the equal sign (\(=\)) makes it a linear equation.
Option (C): \(x - 1\)
This is also an algebraic expression, lacking any relational sign.
Option (D): \(x + 1 \gt 0\)
This is a mathematical statement containing a inequality sign (\(\gt \)). Therefore, it is an inequality, not an equation.

Step 4: Final Answer:
The statement that represents an equation is \(x - 1 = 0\).