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):

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

For (2):

$\begin{gathered} 6x-10>-82 \\ \text{Add 10 to both sides:} \\ 6x>-82+10 \\ 6x>-72 \\ \text{Divide both sides by 6:} \\ x>-\frac{72}{6} \\ x>-12 \end{gathered}$

Therefore, the solution is:

[tex]-12