Question 1107610
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.


<img src = "http://theo.x10hosting.com/2018/012602.jpg" alt="$$$">


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.