Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
-$$5 x + 5 ( 2 x - 7 ) = - 17 - 3 x$$
A) Identity
B) Conditional equation
C) Inconsistent equation

Question

Quizplus · Accepted Answer

This is a conditional equation because it can be simplified to a form where x has a specific solution. Simplifying both sides gives: $5x + 10x - 35 = -17 - 3x$, which further simplifies to $15x - 35 = -17 - 3x$. Adding $3x$ to both sides and adding $35$ to both sides gives $18x = 18$, which simplifies to $x = 1$. This shows that there is a specific condition (when $x = 1$) that makes the equation true, rather than it being true for all values of $x$ (identity) or having no solution at all (inconsistent).

Determine Whether the Equation Is an Identity, a Conditional Equation 5x+5(2x−7)=−17−3x5 x + 5 ( 2 x - 7 ) = - 17 - 3 x5x+5(2x−7)=−17−3x

Determine Whether the Equation Is an Identity, a Conditional Equation $5 x + 5 ( 2 x - 7 ) = - 17 - 3 x$