7x 5/8x+3 gt;4 7x 5/8x+3 4 gt;0 7x 5 4(8x+3)/8x+3 gt;0 7x 5 32x 12/8x+3 gt;0 25x 17/8x+3 gt;0 25x+17/8x+3 lt;0 Case 1:25x+17 gt;0 and 8x+3 lt ...

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

Properties of Inequalities

7 x-5/8 x+3>4

Question

$\frac{7 x - 5}{8 x + 3} > 4$

Open in App

Solution

$\frac{7 x - 5}{8 x + 3} > 4 \frac{7 x - 5}{8 x + 3} - 4 > 0 \frac{7 x - 5 - 4 (8 x + 3)}{8 x + 3} > 0 \frac{7 x - 5 - 32 x - 12}{8 x + 3} > 0 \frac{- 25 x - 17}{8 x + 3} > 0 \frac{25 x + 17}{8 x + 3} < 0 C a s e 1 : 25 x + 17 > 0 a n d 8 x + 3 < 0 x > \frac{- 17}{25} a n d x < \frac{- 3}{8} C a s e 2 : 25 x + 17 > 0 a n d 8 x + 3 < 0 \Rightarrow x < \frac{- 17}{25} a n d x < \frac{- 3}{8} This is not possible. ∴ Hence the solution set is [\frac{- 17}{25}, \frac{- 3}{8}] .$

Suggest Corrections

Similar questions

x

\frac{7 x - 5}{8 x + 3} > 4

\frac{7 x - 5}{8 x + 3} > 4

\frac{7 x - 5}{8 x + 3} > 4

{lim}_{x \to \infty} \frac{2 x^{2} - 3 x + 5}{7 x^{3} - 8 x - 4}

4 x^{5} + 7 x^{4} + 14 x^{3} + 3 x^{2} - 8 x + 6

x^{2} + 3 x + 2

Join BYJU'S Learning Program