Question

Examine the equation-5|1 + 8x| + 9 = -116A: Determine how many solutions this equation has and justify your responseB: Determine what your solutions are for this equation

Answer 1

Part A

The equation has two solutions since it is an absolute equation.

Part B

Given the equation:

`-5|8x+1|+9=-116`

First, subtract 9 from both sides.

`\begin{gathered} -5|8x+1+9-9=-116-9 \\ -5|8x+1|=-125 \end{gathered}`

Next, we divide both sides by -5.

`\begin{gathered} (-5\mleft(|8x+1|\mright))/(-5)=(-125)/(-5) \\ |8x+1|=25 \end{gathered}`

We then solve the absolute value.

`\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=(24)/(8)\text{ or }x=(-26)/(8) \\ x=3\text{ or }-(13)/(4) \end{gathered}`

The solutions for this equation are 3 or -13/4.