Question

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

Answer 1

In the picture below

Explanation:

Edge 2021

Answer 2

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

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

For test point
`x=(4)/(5)`, the inequality is true.

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

Solution:

Given expression is the inequality.

`$(5 x-3)/((x-1)(x+1)) \leq 0`

Substitute x = –2 in the inequality.

`$(5 (-2)-3)/((-2-1)(-2+1) )=(-13)/((-3)(-1) )`

`$=(-13)/(3 )`

< 0

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

Substitute x = 0 in the inequality.

`$(5 (0)-3)/((0-1)(0+1) )=(-3)/((-1)(1) )`

`$=3`

> 0

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

Substitute
`x=(4)/(5)` in the inequality.

`$(5 ((4)/(5) )-3)/((((4)/(5) )-1)(((4)/(5) )+1) )=(1)/((-(1)/(5) )((9)/(5) ) )`

`$=(-25)/(9 )`

< 0

For test point
`x=(4)/(5)`, the inequality is true.

Substitute x = 2 in the inequality.

`$(5 (2)-3)/((2-1)(2+1) )=(7)/((1)(3) )`

`$=(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=(4)/(5)`, the inequality is true.

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