We nbsp;have, nbsp;5x+84 x lt;2⇒5x+84 x 2 lt;0⇒5x+8 24 x4 x lt;0⇒5x+8 8+2x4 x lt;0⇒7x4 x lt;0⇒7xx 4 gt;0 ∴ nbsp;x∈ ∞,0∪4,∞ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Properties of Inequalities

5 x+84-x<2

Question

$\frac{5 x + 8}{4 - x} < 2$

Open in App

Solution

$We have, \frac{5 x + 8}{4 - x} < 2 \Rightarrow \frac{5 x + 8}{4 - x} - 2 < 0 \Rightarrow \frac{5 x + 8 - 2 (4 - x)}{4 - x} < 0 \Rightarrow \frac{5 x + 8 - 8 + 2 x}{4 - x} < 0 \Rightarrow \frac{7 x}{4 - x} < 0 \Rightarrow \frac{7 x}{x - 4} > 0$

$∴ x \in (- \infty, 0) \cup (4, \infty)$

Suggest Corrections

Similar questions

(x^{2} - 5 x) (x^{2} - 5 x - 20) + 84

x

\frac{5 x + 8}{4 - x} < 2

g (x)

f (x) = 5 x^{2} + 4

f (g (3)) = 84

5 (x + 4) - 8 (4 - x) = 25 - 3 (7 - x) + 144

Factorize:
$7 x^{2} + 49 x + 84$

Join BYJU'S Learning Program