[tex]3x-91 > -81\ \ \ \ |+91\\\\3x > 10\ \ \ \ |:3\\\\x > \dfrac{10}{3}\\\\17x-16 > 18\ \ \ \ |+16\\\\17x > 34\ \ \ \ |:17\\\\x > 2\\\\Answer:\ 2 < x < \dfrac{10}{3}\to x\in\left(2,\ \dfrac{10}{3}\right)[/tex]
Answer:
( 2, ∞ )
Step-by-step explanation:
Given compound inequality,
3x-91 > -87 and 17x-16 > 18,
3x > -87 + 91 and 17x > 18 + 16
3x > 4 and 17x > 34
x > [tex]\frac{4}{3}[/tex] and x > 2
Since, if x > [tex]\frac{4}{3}[/tex]
x ∈ ( [tex]\frac{4}{3}[/tex], ∞ )
If x > 2
x ∈ ( 2, ∞ )
Now, x > [tex]\frac{4}{3}[/tex] and x > 2
[tex]\implies (\frac{4}{3}, \infty)\cap (2, \infty)[/tex]
= ( 2, ∞ )
Hence, the possible solution of the given compound inequality is (2, ∞)