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Properties of Inequalities

Solve the fol...

Question

Solve the following system of equations in R.
$\frac{2 x - 3}{4} - 2 \leq \frac{4 x}{3} - 6, 2 (2 x + 3) < 6 (x - 2) + 10$

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Solution

Consider the first inequation,

$\frac{2 x - 3}{4} - 2 \leq \frac{4 x}{3} - 6 \frac{2 x + 3 - 8}{4} \geq \frac{4 x - 18}{3} 3 (2 x - 11) \geq 4 (4 x - 18) 6 x - 33 \geq 16 x - 72 6 x - 16 x \geq - 72 + 33 - 10 x \geq - 39 x \leq \frac{39}{10} . . . (i)$

Consider the second inequation,

$2 (2 x + 3) < 6 (x - 2) + 10 4 x + 6 < 6 x - 12 + 10 4 x - 6 x < - 12 - 6 + 10 - 2 x < - 8 x > 8 . . . (i i)$
From (i) and (ii)there is no solution set of the simultaneous equations.

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