Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$3 ( 12 x + 8 ) = 6 ( 4 x + 22 )$$
A) Contradiction; $\varnothing$
B) Identity; {all real numbers }
C) Conditional; $\{ 9 \}$
D) Conditional; $\{ - 13 \}$

Question

Quizplus · Accepted Answer

Distributing both sides gives $36x + 24 = 24x + 132$. Subtracting $24x$ from both sides results in $12x + 24 = 132$. Subtracting 24 from both sides gives $12x = 108$. Dividing by 12 gives $x = 9$, so the solution set is $\{ 9 \}$.

Decide Whether the Equation Is an Identity, a Conditional Equation 3(12x+8)=6(4x+22)3 ( 12 x + 8 ) = 6 ( 4 x + 22 )3(12x+8)=6(4x+22)

Decide Whether the Equation Is an Identity, a Conditional Equation $3 ( 12 x + 8 ) = 6 ( 4 x + 22 )$