Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 34

Solve the equation $4(2x+7) = 2x + 25 + 3(2x+1)$, and check your solution. If applicable, tell whether the equation is an identity or contradiction.


$
\begin{equation}
\begin{aligned}

4(2x+7) =& 2x + 25 + 3(2x+1)
&& \text{Given equation}
\\
8x + 28 =& 2x + 25 + 6x + 3
&& \text{Distributive property}
\\
8x + 28 =& 8x + 28
&& \text{Combine like terms}
\\
8x - 8x =& 28-28
&& \text{Subtract $(8x + 28)$ from each side}
\\
0 =& 0
&& \text{True}

\end{aligned}
\end{equation}
$


The final line, $0=0$ indicates that the solution set is $\{$ all real numbers $\}$ and the equation $4(2x+7) = 2x + 25 + 3 (2x + 1)$ is an identity.