Question

Which of the following is the correct graph of the solution to the inequality −8 −5x + 2 > −38?

Answer 1

`-8-5x+2 > -38\\\\-5x+(-8+2) > -38\\\\-5x-3 > -38\qquad|+3\\\\-5x > -35\qquad|\text{change the signs}\\\\5x < 35\qquad|:5\\\\x < 7`

Answer 2

x < 6.4

Explanation:

given,

-8 - 5 x + 2 > -38

- 5 x - 6 > -38

adding both side by 6

- 5 x - 6 + 6 > -38 + 6

- 5 x > -32

multiplying both side by (-1)

5 x < 32

on multiplying by negative sign the inequality direction changes

x < 6.4

the graph is shown in the figure attached below. the shaded region shows the required area.