Question

Solve -2x + 1 less than or greater to -7 and describe the graph of the solution.

A x less than or greater to 4; closed circle on 4, shading to the left
B x greater than or equal to 4; closed circle on 4, shading to the right
C x greater than or equal to 4; open circle on 4, shading to the right
D x less than or greater to 4; open circle on 4, shading to the left

Answer 1

I'll look at the cases separately (though they're very similar):
- 2x +1 < -7 | -1
-2x < -8 | : (-4)
x > 4 (< becomes > when multiplying with a negative number)
That means if -2x +1 < -7 is true, it follows that x is greater than 4.

-2x+1 > -7 | -1
-2x > -8 | :(-4)
x < 4 (> becomes < when multiplying with a negative number)
That means if -2x +1 > -7 is ture, it follows that x is smaller than 4.

Hence, the inequality is true if x is not 4. This means that your solution is anything except 4. I'm not quite sure what you mean by "closed/open" circle or "shading to the left", but if it means what I think it means then it is an open circle. I have no idea what "shading to the left" means. Sorry, English is not my native language.

Answer 2

But anyway, I'm quite sure that the right answer is D

Answer 3

@Stiwan thank you!