Which of these is an example of a literal equation?
A. [tex]$a x-b y=k$[/tex]
B. [tex]$5 x+9 y$[/tex]
C. [tex]$4+12=4^2$[/tex]
D. [tex]$8-2 x=14$[/tex]
Answer (1)
A literal equation contains multiple variables representing known values.
Option A, a x − b y = k , fits this description.
Options B, C, and D do not fit the description of a literal equation.
Therefore, the answer is A .
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 description.
Analyzing Option A Option A: a x − b y = k . This equation contains multiple variables ( a , x , b , y , k ), which is characteristic of a literal equation, where variables can represent known values.
Analyzing Option B Option B: 5 x + 9 y . This is an expression, not an equation, so it cannot be a literal equation.
Analyzing Option C Option C: 4 + 12 = 4 2 . This is a numerical equation with no variables, so it is not a literal equation.
Analyzing Option D Option D: 8 − 2 x = 14 . This is an equation with one variable ( x ), and it is not a literal equation because it is meant to be solved for a specific value of x .
Conclusion Therefore, the correct answer is Option A, as it is an equation with multiple variables representing known values.
Examples
Literal equations are used in physics and engineering to represent 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 the motion. This is useful for predicting the motion of objects under constant acceleration.
