Which of the following is NOT true?
2024
Which of the following is NOT true?
- A.
3 + 4 × 5 is not a mathematical expression
- B.
Operations of multiplication can be done on mathematical expressions
- C.
The expression (x^2 + 10x + 25) cannot be simplified further
- D.
The value of the variable in an equation which satisfy the equation is called a solution of the equation
Show answer & explanation
Correct answer: A
Concept: A mathematical expression is any combination of numbers and/or variables joined by operations such as +, −, ×, ÷, with no equals sign. Simplifying an expression means writing it in its reduced standard (expanded) form; rewriting it as a product of factors (factorisation) is a related but separate operation. A solution (or root) of an equation is a value of the variable that satisfies that equation.
Application: Check the claim about "3 + 4 × 5" against the definition above. It is built from the numbers 3, 4, 5 and the operations + and × — that is exactly what a mathematical expression is, so it certainly IS one. The statement claiming it is "not a mathematical expression" is therefore false, and since the question asks for the statement that is NOT true, this is the one being asked for.
Contrast (the other three statements are all true):
"(x2 + 10x + 25) cannot be simplified further" — true; the expression is already in its simplified, standard expanded polynomial form. Rewriting it as (x + 5)2 is factorisation, a distinct operation from simplification, so the statement about simplification still stands.
"Operations of multiplication can be done on mathematical expressions" — true; × is one of the basic operations expressions are built from, exactly as seen inside "3 + 4 × 5" itself.
"The value of the variable in an equation which satisfies the equation is called a solution of the equation" — true; this is exactly the standard definition of a solution (root) of an equation.
Cross-check: Apply the same expression-definition test to any similar combination, such as 2 + 3 or 6 × 7 — none of these fail to qualify as an expression either, confirming that calling "3 + 4 × 5" not an expression is the one false claim among the four statements.