Question

1. Which of the following is equivalent to the inequality - 8 > 8x + 16 ?

Α. χ < -1
Β. x >-1
C. χ<-3
D. χ> 3
Ε. χ<3

Answer 1

x < -3 is the solution for the given inequality - 8 > 8x + 16.

Explanation:

Here, the given inequality is - 8 > 8x + 16

Now, we know if equal (positives) are added, subtracted multiplied or divided on both sides of in equality, the signs remain unchanged.

⇒ - 8 > 8x + 16 is equivalent to - 8 + 8 > 8x + 16 + 8

or, 0 > 8x + 24

⇔ -8x > 8x + 24 - 8x

⇔ -8 x > 24

or,
`(-8x)/(-8)   <   (24)/(-8)` (REVERSE SIGN as dividing by a a negative number)

or, x < -3

or, x < -3 is the solution for the given inequality.