Which of these is an example of a literal equation?
A. $4+12=4^2$
B. $a x-b y=k$
C. $5 x+9 y$
D. $8-2 x=14$
Answer (1)
A literal equation is an equation where variables represent known values.
Option A is a numerical equation.
Option B, a x − b y = k , is a literal equation.
Option C is an expression, not an equation.
Option D is an equation with one variable.
The correct answer is B .
Explanation
Understanding Literal Equations A literal equation is an equation where variables represent known values. We need to identify which of the given options fits this definition.
Analyzing Option A Option A: 4 + 12 = 4 2 simplifies to 16 = 16 . This is a numerical equation, not a literal equation, as it contains only numbers.
Analyzing Option B Option B: a x − b y = k is an equation with multiple variables ( a , b , x , y , and k ). In a literal equation, the variables represent known values. This option fits the definition of a literal equation.
Analyzing Option C Option C: 5 x + 9 y is an expression, not an equation, as it does not have an equals sign.
Analyzing Option D Option D: 8 − 2 x = 14 is an equation with one variable ( x ). While it is an equation, it is not a literal equation because it aims to solve for the unknown variable x , rather than expressing a relationship between known quantities.
Conclusion Based on the analysis, option B, a x − b y = k , is the literal equation because it is an equation where variables represent known values.
Examples
Literal equations are used in physics and engineering to express relationships between different physical quantities. For example, the equation v = u + a t relates the final velocity ( v ) of an object to its initial velocity ( u ), acceleration ( a ), and time ( t ). By rearranging this literal equation, we can solve for any of the variables in terms of the others, allowing us to easily calculate different aspects of motion.
