Question

Determine whether the equation is an identity, a conditional, or an inconsistent equation. 16x + 15(x+1) = 31(x+1)-16

Answer 1

We are to determine whether the given equation is an identity, a conditional, or an inconsistent equation.

`\begin{gathered} 16x\text{ + 15(x+1) = 31(x+1)-16} \\ 16x\text{ + 15x + 15 = 31x + 31 - 16} \\ 31x\text{ + 15 = 31x + 15} \end{gathered}`

An identity is an equation satisfied by every number that is a meaningful replacement for the variable.

A conditional equation is an equation satisfied by some numbers but not others.

An Inconsistent equation is an equation that has no solution.

Since the left hand side is equal to the right hand side, then the given equation is an Identity.