Given : A inequality is given to us . The inequality is 19 ≥ t + 18 ≥ 11 .
To Find : The correct option between the given ones . To write the compound inequality with integers .
Solution : The given inequality to us is 19 ≥ t + 18 ≥ 11 . Let's simplify them seperately .
[tex]\red{\tt Case\:1}[/tex]
⇒ 19 ≥ t + 18 .
⇒ t + 18 ≤ 19 .
⇒ t ≤ 19 - 18 .
⇒ t ≤ 1 = 1 ≥ t . ..................(i)
[tex]\red{\tt Case\:2}[/tex]
⇒ t + 18 ≥ 11 .
⇒ t ≥ 11 - 18.
⇒ t ≥ -7 . ....................(ii)
On combing (i) & (ii) .
[tex]\Large\boxed{\green{\bf \red{\longmapsto} 1 \geqslant t \geqslant -7 }}[/tex]
This means that t is less than or equal to 1 but greater than or equal to (-7) .
