Question

3x-91>-87 AND 17x-16>18

Answer 1

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 > $\frac{4}{3}$ and x > 2

Since, if x > $\frac{4}{3}$

x ∈ ( $\frac{4}{3}$, ∞ )

If x > 2

x ∈ ( 2, ∞ )

Now, x > $\frac{4}{3}$ and x > 2

$\implies (\frac{4}{3}, \infty)\cap (2, \infty)$

= ( 2, ∞ )

Hence, the possible solution of the given compound inequality is (2, ∞)

Answer 2

$3x-91 > -81\ \ \ \ |+91\\\\3x > 10\ \ \ \ |:3\\\\x > \dfrac{10}{3}\\\\17x-16 > 18\ \ \ \ |+16\\\\17x > 34\ \ \ \ |:17\\\\x > 2\\\\Answer:\ 2 < x < \dfrac{10}{3}\to x\in\left(2,\ \dfrac{10}{3}\right)$