Solve the inequalities for real x. \[\frac{x}{3}>\frac{x}{2}+1\] - India Site

Solve the inequalities for real x. \[\frac{x}{3}>\frac{x}{2}+1\]

Class 11 | Exercise 6.1 | Linear Inequalities | Maths | NCERT

Solve the inequalities for real x. \[\frac{x}{3}>\frac{x}{2}+1\]

Solution:

From the question it is given that \[\frac{x}{3}>\frac{x}{2}+1\]

After rearranging and taking LCM we get,

\[\left( \frac{2x-3x}{6} \right)>1\]

\[-x/6>1\]

\[-x>6\]

\[x<-6\]

The solutions of \[\frac{x}{3}>\frac{x}{2}+1\]are defined by all the real numbers less than \[-6\].

Therefore, the required solution set is \[(-\infty ,-6)\]

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