Question

could someone help me understand this /
Inequalities on a number line

Answer 1

please help!

Answer 2

The < same means less then only. The < sign with a line under it means less then OR equal to. And the > sign means greater then only, while the > sign with a line under it means greater then OR equal to. Hope I helped!

Answer 3

thanks..

Answer 4

is that what you needed help with?

Answer 5

well not really .. just reading it on a number line.

Answer 6

nevermind! I got it!!!! thanks soooo much. I see if its a closed dot its going to be greater than or equal to or less than equal too .
and if its a open dot its just regular greater than or less than

Answer 7

okay so
1.Simplify the inequality you're going to graph. Multiply out anything that's in parentheses, and combine numbers that are unattached to variables.
-2x2 + 5x < -6(x + 1)
-2x2 + 5x < -6x - 6

2.Move all terms to one side so the other is zero. It will be easiest if the highest power variable is positive. Combine common terms (such as -6x and -5x).
0 < 2x2 -6x - 5x - 6
0 < 2x2 -11x - 6

3.Solve for the variables. Pretend that the inequality sign is an equal sign, and find all values of the variable. If necessary, solve by factoring.
0 = 2x2 -11x - 6
0 = (2x + 1)(x - 6)
2x + 1 = 0, x - 6 = 0
2x = -1, x = 6
x = -1/2, x = 6

4.Draw a number line including the variable solutions (in order).

5.Draw a circle on the points. If the inequality symbol is "less than" (<) or "more than" (>), draw an empty circle over the variable solution(s). If it means "less than or equal to" (≤) or "more than or equal to" (≥), then fill in the circle.

In this case the equation was greater than zero, so use open circles.

6.Test your solution. Take a number from each of the resulting intervals and plug it back into the inequality. If you get a true statement once solved, shade this region of the number line.

In the interval from (-∞,-1/2) we will take -1 and plug it into the original inequality.
0 < 2x2 -11x - 6
0 < 2(-1)2 -11(-1) - 6
0 < 2(1) + 11 - 6
0 < 7
Zero is less than 7 is correct, so shade (-∞, -1/2) on the number line.

Next, on the interval from (-1/2, 6) we will use zero.
0 < 2(0)2 -11(0) - 6
0 < 0 + 0 - 6
0 < -6
Zero is not less than negative six, so do not shade (-1/2,6).

Lastly, we will take 10 from the interval (6,∞).
0 < 2(10)2 - 11(10) + 6
0 < 2(100) - 110 + 6
0 < 200 - 110 + 6
0 < 96
Zero is less than 96 is correct, so shade (6,∞) as well.

Use arrows on the end of shading to indicate that the interval continues into infinity. The completed number line...hope this is what you meant lol

Answer 8

oh lol cx well youre welcome can i have a medal? :3

Answer 9

im new to this how do u give medals?

Answer 10

all you have to do is press best response and it gives the person a medal but you can only give one person the medal and welcome to open study :3

Answer 11

aww. so ur a teacher

Answer 12

no lol im only in 7th grade xD