Question

Which of the given statements is true?

• A. An algebraic expression has a LHS and a RHS.
• B. An equation cannot have a variable.
• C. All equations are identities.
• D. All identities are equations.

Answer 1

The correct option is D All identities are equations.

An algebraic expression is a combination of variables and constants with a mathematical operator.
When an expression is equated to a quantity (which can be an expression, or a variable or a constant), then it is called an equation.
An equation has two sides: Left hand side (LHS) and Right hand side (RHS). But an expression does not have any sides.
An identity is an equality, which is true for all values of the variables in the equality.
Every identity is an equation (as per the definition), but all equations need not be identities.
For example, $a+2=3+b$ is an equation but not an identity as it does not hold true for each set of values of a and b.