Question

list the solution set of inequation​

Answer 1

$\huge {\mathfrak {\underline {\pink {Solution:}}}}$

$\large {\mathtt {\boxed {\blue {Case \: 1:}}}}$

$\large { - 1 \leqslant 3 \times 4x}$

=⟩ $\large {- 1 -3\leqslant 4x }$

=⟩ $\large {- 4\leqslant 4x }$

=⟩ $\large { \frac{ - 4}{4} \leqslant x}$

=⟩ $\large {-1 \leqslant x}$

$\large {\mathtt {\boxed {\blue {Case \: 2:}}}}$

$\large {3 + 4x < 23 }$

=⟩ $\large { 4x < 23 - 3 }$

=⟩ $\large { 4x < 20 }$

=⟩ $\large {x < \frac{20}{4} }$

=⟩ $\large {x < 5 }$

$\large {\mathtt {\boxed {\blue {Final \: inequation:}}}}$

On combining both, case 1 and case 2, we get

$\large {- 1 \leqslant x < 5}$

So according to this our solution set will be:

set = { -1, 0, 1, 2, 3, 4}

For number line, refer attachment.

Hope this helped you, thanks for posting :)