Question

Which of the following is an equation?
a) \[x + 1\]
b) \[x - 1\]
c) \[x - 1 = 0\]
d) \[x + 1 > 0\]

Answer 1

Hint: Here we are asked to find which of the given options is an equation. An algebraic expression is a combination of variables and constants connected by the arithmetic operation whereas an equation is an equality statement that involves one or more variables. Using these definitions, we can separate the algebraic expression and equations.

Complete step-by-step solution:
We aim to find whether the given options are an equation or not. We will find it by considering the options one by one by using the definition of an equation.
An equation is a statement of equality that involves one or more variables.
Let us see the options, option (a) \[x + 1\] as we can see that this is an algebraic expression not an equation because it does involve variables and arithmetic operations but it does not represent a statement of equality. That is the expression does not equate to anything.
Option (b) \[x - 1\] similarly this is also an algebraic expression because it does involve variables and arithmetic operations but it does not represent a statement of equality.
Option (c) \[x - 1 = 0\] this is an equation as we can see that it is a statement of equality that is an expression equated to zero. The expression on the left side of the equal sign is called the left-hand side and that of the right side is called the right-hand side.
Option (d) \[x + 1 > 0\] is not an equation since it is not the statement of equality. It contains an inequality sign so it does not come under equations. It is an equation of inequality.
Hence, option (c) \[x - 1 = 0\] is the right answer.

Note: A symbol having fixed values are called constants and a symbol that takes various numerical values are called variables. An algebraic expression contains variables, constants, and arithmetic operations. But an equation is a statement of equality. The statement that involves the equal to sign is called the statement of equality.