Question

olve the equation. If there is more than one solution, separate them with a comma.| 7x+2|=37

Answer 1

Given:

$|7x+2\left|=37\right?$

To find: The solutions

Explanation:

Since it is an absolute equation.

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

For the Positive case,

$\begin{gathered} 7x+2=37 \\ 7x=35 \\ x=5 \end{gathered}$

For the negative case,

$\begin{gathered} -(7x+2)=37 \\ 7x+2=-37 \\ 7x=-39 \\ x=-\frac{39}{7} \end{gathered}$

Final answers: The solutions are,

$x=-\frac{39}{7},5$