Question

The set of all values of x satisfying the inequations 2x
+3 > 3x - 1 and 4x-1 > 7 is

Answer 1

ANSWER

(x 2 −5x+5) x 2+4x−60=1

First possibility is x 2+4x−60=0 x=−10,6

Seond possibility is x 2 −5x+5=1 x=1,4

Third Possibility x 2 −5x+5=−1 x=2,3

substitute x=3 it will give odd number in x +4−60

So x=2 is only acceptable.

Sum of the integers =−10+4+1+6+2=3

Answer 2

Given inequalities

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

$4x-1 > 7$ .............(2)

Simplifying the inequality (1) and we get

$2x+3 > 3x - 1\\\Rightarrow 2x+3-3 > 3x-1-3\\\Rightarrow 2x > 3x-4\\\Rightarrow 2x-2x+4 > 3x-2x-4+4\\\Rightarrow 4 > x\\\Rightarrow x < 4$

Simplifying the inequality (2) and we get

$4x-1 > 7\\\Rightarrow 4x-1+1 > 7+1\\\Rightarrow 4x > 8\\\Rightarrow x > \frac{8}{4}\\\Rightarrow x > 2$

Hence, from the inequalities we get

$2 < x < 4\\i.e., x \in (2,4)$

therefore, the correct option is (2, 4).

To learn more about inequality from the given link

https://brainly.in/question/17868857

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