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Question 1107610: Please help. I'm trying to solve and graph the inequality.
I'm confused on it because the b is negative. I don't think it can be graphed. Here's what I have. Can you please tell me if I'm correct.
-8-b less than equal to -8
-8+8-b less than equal to -8+8
-b less than equal to 0
Thank you.
Found 2 solutions by jim_thompson5910, Theo:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Note: you can type "<=" without quotes to mean "less than or equal to". Similarly, ">=" means "greater than or equal to"
You have the right steps which are
-8 - b <= -8
-8 - b+8 <= -8+8
-b <= 0
The last step to do is multiply both sides by -1. This will flip the inequality sign from a "less than or equal to" sign to a "greater than or equal to" sign
So we go from this
-b <= 0
to this
b >= 0
after multiplying both sides by -1
The solution set is the set of all b values such that b is zero or a value larger than zero
To graph this, plot a closed circle at 0 on the number line. Then shade to the right of the closed circle. The closed circle indicates we include the endpoint as part of the solution set.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! your equation is -8 - b <= -8
as you did, add 8 to both sides of the equation to get -8 + 8 - b <= -8 + 8.
simplify to get -b <= 8.
to solve for b, multiply both sides of this equation by -1 to get b >= -8
you have to remember that, when you multiply or divide both sides of an inequality by a negative numer, the inequality reverses.
here's a couple of examples;
5 < 8
multiply both sides by -1 and you get -5 > -8.
multiply both sides by -2 and you get -10 > -16.
divide both sides of -10 > -16 by -2 and you get 5 < 8.
your solution is -b <= 0 which is the same as b >= 0.
to graph this, let x = b and the equation becomes x >= 0.
you would draw the line x = 0 on the graph and then shade the area of the graph that is to the right of x = 0.
your graph would look like this.
to see if your solution is corect, go back to the original equation and check to see if the equation is true when b is >= 0 and not true when b is < 0.
your original equation is -8 - b <= -8
when b = 0, this equation becomes -8 <= -8 which is true.
when b is less than 0, like say -1, this equation becomes -8 -(-1) <= -8.
this simplifies to -8 + 1 <= -8 which becomes -7 <= -8 which is false.
when b is greater than 0, like say 1, this equation becomes -8 - 1 <= -8.
this simplifies to -9 <= -8 which is true.
the inequality is true when b is greater than or equal to 0.
the inequality is false when b is less than 0.
when your variable of interest is negative, multiply both sides of the inequality or the equation by -1 to make it positive.
with an equation, the equality will still hold.
with an inequality, the inequality reverses.
if -x = y, then x = -y.
if -x >= y, then x <= -y.
if -x > y, then x < -y.
if -x <= y, then x >= -y.
if -x < y, then x > -y.
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