Question

1. Find the set of values of x for which (2x + 1)(4 - x) > (x - 4)(2x - 3)​

Answer 1

Answer:

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Answer 2

Answer:

The answer is $x<\frac{1}{2}$  or $x>4$

Step-by-step explanation:

Given inequality is

               $(2x+1)(4-x)>(x-4)(2x-3)$

            $\Rightarrow (2x+1)(4-x)-(x-4)(2x-3)>0$

Caveat:Don't cancel common terms from both sides, as we don't know its sign

          $\Rightarrow -(2x+1)(x-4)-(x-4)(2x-3)>0\\\Rightarrow (x-4)(-2x-1-2x+3)>0\\\Rightarrow (x-4)(2-4x)>0$

Divide both sides by -2 (sign of inequality will change as -2 is negative)

        $\Rightarrow (x-4)(2x-1)<0\\\Rightarrow x<\frac{1}{2} \text { or }x>4$