The solutions are 2, 4
Explanation:[tex]\begin{gathered} Given: \\ -9\text{ - 8\mid2x - 6\mid= -25} \\ We\text{ need to solve for x} \end{gathered}[/tex]
collect like terms by adding 9 to both sides:
[tex]\begin{gathered} -9\text{ + 9 -8\mid2x - 6\mid = -25 + 9} \\ 0\text{ -8\mid2x - 6\mid = -25 + 9} \\ −8∣2x−6∣=-16 \end{gathered}[/tex]
divide both sides by -8:
[tex]\begin{gathered} \frac{-8\left|2x\text{ - 6\mid}\right?}{-8}\text{ = }\frac{-16}{-8} \\ division\text{ of same signs give positive sign} \\ \left|2x\text{ - 6\mid = 2}\right? \end{gathered}[/tex]
We are left with an absolute value function. We will get two results from it
[tex]\begin{gathered} \left|2x\text{ - 6\mid = 2 is represented as 2x -6 = 2 or 2x - 6 = -2}\right? \\ We\text{ will for x solve in each of them:} \\ 2x−6=2 \\ Add\text{ 6 to both sides:} \\ 2x\text{ - 6 + 6 = 2 + 6} \\ 2x\text{ = 8} \\ divide\text{ both sides by 2:} \\ \frac{2x}{2}=\text{ }\frac{8}{2} \\ x\text{ = 4} \end{gathered}[/tex][tex]\begin{gathered} 2x\text{ - 6 = -2} \\ Add\text{ 6 to both sides:} \\ 2x\text{ - 6 +6 = -2+6} \\ 2x\text{ = 4} \\ \text{ } \\ divide\text{ both sides by 2:} \\ \frac{2x}{2}\text{ = }\frac{4}{2} \\ division\text{ of same signs give positive sign} \\ x\text{ = 2} \end{gathered}[/tex]
The solutions are 2, 4
