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Q.
The solution set of the inequalities $3x - 7 > 2(x - 6)$ and $6 - x > 11 - 2x$, is
Linear Inequalities
Solution:
We have $3x - 7 > 2(x - 6)$
$\Rightarrow 3x - 7 > 2x - 12$
Transferring the term $2x$ to $L.H.S.$ and the term $\left(-7\right)$ to $R.H.S., 3x - 2x > -12 + 7$
$\Rightarrow x>-5\,...\left(i\right)$
and $6-x >11-2x$
Transferring the term $\left(-2x\right)$ to $L.H.S$. and the term 6 to $R.H.S.,\quad -x + 2x > 11 - 6$
$\Rightarrow x > 5\,...\left(ii\right)$
Draw the graph of inequations (i) and (ii) on the number line,
Hence, solution set of the equations are real numbers, $x$ lying on greater than 5 excluding 5. i.e., $x > 5 \therefore $ Solution set is $(5, \infty)$
