Question

Type in true or false statement... Help ASAP please

Answer 1

For test point x = –2, the inequality is true.

For test point x = 0, the inequality is false.

For test point $x=\frac{4}{5}$, the inequality is true.

For test point x = 2, the inequality is false.

Solution:

Given expression is the inequality.

$\frac{5 x-3}{(x-1)(x+1)} \leq 0$

Substitute x = –2 in the inequality.

$\frac{5 (-2)-3}{(-2-1)(-2+1) }=\frac{-13}{(-3)(-1) }$

                            $=\frac{-13}{3 }$

                            < 0

For test point x = –2, the inequality is true.

Substitute x = 0 in the inequality.

$\frac{5 (0)-3}{(0-1)(0+1) }=\frac{-3}{(-1)(1) }$

                      $=3$

                      > 0

For test point x = 0, the inequality is false.

Substitute $x=\frac{4}{5}$ in the inequality.

$\frac{5 (\frac{4}{5} )-3}{((\frac{4}{5} )-1)((\frac{4}{5} )+1) }=\frac{1}{(-\frac{1}{5} )(\frac{9}{5} ) }$

                            $=\frac{-25}{9 }$

                            < 0

For test point $x=\frac{4}{5}$, the inequality is true.

Substitute x = 2 in the inequality.

$\frac{5 (2)-3}{(2-1)(2+1) }=\frac{7}{(1)(3) }$

                      $=\frac{7}{3 }$

                      > 0

For test point x = 2, the inequality is false.

Hence,

For test point x = –2, the inequality is true.

For test point x = 0, the inequality is false.

For test point $x=\frac{4}{5}$, the inequality is true.

For test point x = 2, the inequality is false.