Explanation
To solve the given inequality, we will have
[tex]3|x-4|-5<10[/tex]To solve the question
we will follow the steps below
Step 1:
[tex]\begin{gathered} \mathrm{Add\:}5\mathrm{\:to\:both\:sides} \\ 3\left|x-4\right|-5+5<10+5 \end{gathered}[/tex]Step 2:
[tex]\begin{gathered} \mathrm{Simplify} \\ 3\left|x-4\right|<15 \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \mathrm{Divide\:both\:sides\:by\:}3 \\ \frac{3\left|x-4\right|}{3}<\frac{15}{3} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} \mathrm{Simplify} \\ \left|x-4\right|<5 \end{gathered}[/tex]step 5
[tex]\begin{gathered} \mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a \\ -5Step 6[tex]x>-1\quad \mathrm{and}\quad \:x<9[/tex]Thus we have the answer as
[tex]-1