Solve the following inequalities for real x. (2x− 3/4) -3< (x-4/3) −2, x ∈ R. ​

Question

Solve the following inequalities for real x. 

\(\frac{2x-3}{4}\) − 3< \(\frac{x-4}{3}\) −2, x ∈ R.

Answer 1

We have, 

\(\frac{2x−3}{4}\)−3 < \(\frac{x−4}{3}\)−2,

⟹ \(\frac{2x−9}{4}\) < \(\frac{x−10}{3}\)

⟹ \(\frac{x}{2}\) − \(\frac{x}{3}\) < \(\frac{−10}{3}\) + \(\frac{9}{4}\)

[Transposing \(\frac{x}{2}\)to LHS and \(\frac{9}{4}\) to RHS]

⟹ \(\frac{x}{6}\) < \(\frac{13}{12}\)

⟹ x < \(\frac{13}{2}\)

∴ x ∈ (−∞, \(\frac{13}{2}\))