Question

solving absolute value inequalities
`8 - 9 |6x - 10| \ \textgreater \ - 82`please help with steps, I keep getting stuck on this one

Answer 1

`\begin{gathered} -|6x-10|>-82 \\ \text{Multiply both sides by -1:} \\ |6x-10|<82 \\ \text{Split into two equations:} \\ 6x-10<82\text{ (1)} \\ 6x-10>-82\text{ (2)} \\ \end{gathered}`

For (1):

`\begin{gathered} 6x-10<82 \\ \text{Add 10 to both sides:} \\ 6x<82+10 \\ 6x<92 \\ \text{Divide both sides by 6:} \\ x<(92)/(6) \\ x<(46)/(3) \\ \end{gathered}`

For (2):

`\begin{gathered} 6x-10>-82 \\ \text{Add 10 to both sides:} \\ 6x>-82+10 \\ 6x>-72 \\ \text{Divide both sides by 6:} \\ x>-(72)/(6) \\ x>-12 \end{gathered}`

Therefore, the solution is:

[tex]-12