Part A
The equation has two solutions since it is an absolute equation.
Part B
Given the equation:
[tex]-5|8x+1|+9=-116[/tex]First, subtract 9 from both sides.
[tex]\begin{gathered} -5|8x+1+9-9=-116-9 \\ -5|8x+1|=-125 \end{gathered}[/tex]Next, we divide both sides by -5.
[tex]\begin{gathered} \frac{-5\mleft(|8x+1|\mright)}{-5}=\frac{-125}{-5} \\ |8x+1|=25 \end{gathered}[/tex]We then solve the absolute value.
[tex]\begin{gathered} 8x+1=25\text{ or }8x+1=-25 \\ 8x=-1+25\text{ or }8x=-1-25 \\ 8x=24\text{ or }8x=-26 \\ x=\frac{24}{8}\text{ or }x=\frac{-26}{8} \\ x=3\text{ or }-\frac{13}{4} \end{gathered}[/tex]The solutions for this equation are 3 or -13/4.
