The set of all real values of x satisfying th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given the inequality: $\frac{8x^2-14x-9}{3x^2-7x-6} > 2$ \ Subtract $2$ from both sides: $\frac{8x^2-14x-9}{3x^2-7x-6} - 2 > 0$ \ $\frac{8x^2-14

Vedclass · Accepted Answer

$(-\infty, -2/3) \cup (3, \infty)$

Vedclass · Answer

(D) Given the inequality: $\frac{8x^2-14x-9}{3x^2-7x-6} > 2$ \ Subtract $2$ from both sides: $\frac{8x^2-14x-9}{3x^2-7x-6} - 2 > 0$ \ $\frac{8x^2-14x-9 - 2(3x^2-7x-6)}{3x^2-7x-6} > 0$ \ $\frac{8x^2-14x-9 - 6x^2+14x+12}{3x^2-7x-6} > 0$ \ $\frac{2x^2+3}{3x^2-7x-6} > 0$ \ Since $2x^2+3$ is always positive for all real $x$,the inequality holds if $3x^2-7x-6 > 0$ \ Factor the denominator: $3x^2-9x+2x-6 = 3x(x-3)+2(x-3) = (3x+2)(x-3) > 0$ \ The critical points are $x = -2/3$ and $x = 3$ \ Testing the intervals $(-\infty, -2/3)$,$(-2/3, 3)$,and $(3, \infty)$,the expression is positive in $(-\infty, -2/3) \cup (3, \infty)$.

The set of all real values of $x$ satisfying the inequation $\frac{8x^2-14x-9}{3x^2-7x-6} > 2$ is

Similar Questions

For a positive integer $n$,the inequality $10^{n - 2} > 81n$ holds true if:

$A$ manufacturer has $600 \text{ litres}$ of a $12 \%$ solution of acid. How many litres of a $30 \%$ acid solution must be added to it so that the acid content in the resulting mixture will be more than $15 \%$ but less than $18 \%$?

Find all pairs of consecutive even positive integers,both of which are larger than $5$,such that their sum is less than $23$.

Solve $\frac{1 - |x|}{2 - |x|} \ge 0$.

$A$ triangle is formed by the $X$-axis,$Y$-axis,and the line $3x + 4y = 60$. The number of points $P(a, b)$ which lie strictly inside the triangle,where $a$ is an integer and $b$ is a multiple of $a$,is $...........$

Vedclass Test Series

Exam Paper Generator

Online Exam Module