Final Answer:
The given expression 3(4g+11)−12g−33=0, is a conditional equation. The solution set for g is all real numbers.
Step-by-step explanation:
In mathematics, a conditional equation is an equation that is true for some values of the variable(s) and false for others. To determine the nature of this equation, let's simplify it step by step. First, distribute the 3 on the left side of the equation:
12
�
+
33
−
12
�
−
33
=
0
12g+33−12g−33=0
Combining like terms, we get
0
=
0
0=0, which is a true statement. This means that the equation is always true, regardless of the value chosen for
�
g. Therefore, the solution set for
�
g is all real numbers.
The fact that the simplified equation is always true indicates that any real number substituted for
�
g will satisfy the equation. This makes it a conditional equation. In contrast, an identity is an equation that is true for all values of the variable, and a contradiction is an equation that is never true. In this case, the equation is satisfied by all values of
�
g, making it a conditional equation with an infinite solution set.