Question

Find the solution for x if |7x + 5|= 19. Where | | denotes the absolute value

Answer 1

We have the following expression:

$|7x+5|=19$

where the bars | | denote the absolute value.

This absolute value equation implies that we have 2 cases:

$\begin{gathered} \text{case A) 7x+5=19} \\ \text{case B) 7x+5=-19} \end{gathered}$

Case A)

In this case, if we move +5 to the right hand side, we get

$\begin{gathered} 7x=19-5 \\ 7x=14 \end{gathered}$

Now, if the move the coefficient of x to the right hand side, we have

$\begin{gathered} x=\frac{14}{7} \\ x=2 \end{gathered}$

that is, the solution for this case is x=2

Case B).

In this case, if we move +5 to the right hand side, we obtain

$\begin{gathered} 7x=-19-5 \\ 7x=-24 \end{gathered}$

Finally, f the move the coefficient of x to the right hand side, we get

$\begin{gathered} x=-\frac{24}{7} \\ \end{gathered}$

that is, the solution for this case is x=-24/7

Therefore, the solution for the problem is

$x=2\text{ and x=-}\frac{24}{7}$