Given inequality,
[tex] \\ \qquad \longrightarrow \: \sf{19 > -4p-5} \\ \\ [/tex]
Adding 5 to both sides we get :
[tex] \\ \qquad \longrightarrow \: \sf{19 + 5 > -4p-5 + 5} \\ \\ [/tex]
[tex] \qquad \longrightarrow \: \sf{24 > -4p \: \ \cancel{- \: 5} \: \cancel{+ \: 5}} \\ \\ [/tex]
[tex] \qquad \longrightarrow \: \sf{24> -4p} \\ \\ [/tex]
Dividing both sides by (-4) we get :
[tex] \\ \qquad \longrightarrow \: \sf{ \frac{24}{ - 4} > \frac{ - 4p}{ - 4} } \\ \\ [/tex]
[tex]\qquad \longrightarrow \: \sf{ - 6 < p} \\ \\ [/tex]
We can also write it as,
[tex] \\ \qquad \longrightarrow \: \sf{ p > - 6} \\ \\ [/tex]
Given the inequation:
[tex]{:\implies \quad \sf 19>-4p-5}[/tex]
Adding 5 to both sides:
[tex]{:\implies \quad \sf 19+5>-4p}[/tex]
Divide both sides by -4, also, we are dividing both sides by a -ve number, so the sign of the inequation will change to <
[tex]{:\implies \quad \sf -\dfrac{24}{4}<p}[/tex]
[tex]{:\implies \quad \sf p>-6\:\:\longrightarrow \boxed{\bf{p\in (-6,\infty)}}}[/tex]
