To determine which of the given options is a literal equation, we first need to understand what a literal equation is. A literal equation is an equation that involves multiple variables. These variables represent unknown quantities, and the equation shows the relationship between them. Generally, literal equations do not immediately resolve to numerical values; instead, they express variables in terms of other variables.
Let's analyze each given option:
A. [tex]$3x - 4y$[/tex]
- This expression involves variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex], but it is not an equation because it lacks an equality sign (=). Therefore, it cannot be a literal equation.
B. [tex]$6 + 30 = 6^2$[/tex]
- This is an equation involving numeric values. There are no variables involved, making it an arithmetic equation rather than a literal one.
C. [tex]$12 = 9 + 3x$[/tex]
- This is an equation involving one variable [tex]\(x\)[/tex] and numeric values. It equalizes a numeric value to an expression involving a variable, making it a conditional equation rather than a literal equation.
D. [tex]$ax - by = k$[/tex]
- This is an equation involving multiple variables [tex]\(a\)[/tex], [tex]\(x\)[/tex], [tex]\(b\)[/tex], and [tex]\(y\)[/tex], as well as a constant [tex]\(k\)[/tex]. It expresses a relationship between these variables. This fits the description of a literal equation.
Based on this analysis, the correct choice is:
D. [tex]\(ax - by = k\)[/tex]
Thus, the answer is 4.
