Question

Which iniquality is represented by the graph? If you can do the top ones thanks too:) please show work if there is any:)

Answer 1

With simple inequalities like this, all you have to do is rearrange to get the numbers on one side of the side and an x on the other;
You can treat the sign like an equals sign but remember one rule;
If you ever multiply or divide both sides of the equation by a negative number, swap the sign (if it's ≤, then make it ≥ and vice versa);
So, for the questions above:

29.
-x/2 ≤ -4
-x ≤ -8
x ≥ 8

30.
I'm unsure what's being asked for this question.

31.
For these graphs, just look at whether the direction of the line from its origin (the small circle part) is going up the number line to the larger numbers or towards the smaller (more negative) numbers;
In this case, the line starts at 10 and goes up the number line;
The circle that denotes the start of the line is unshaded, this means the inequality being represented is a > or <, not a ≥ or ≤, which is shown by a circle that is shaded;
Looking at the line (representing x-values) therefore, we can determine the inequality it represents is:
x > 10;
so now we just need to rearrange the options given and see which is the same as x > 10;
In this case it is option A:
x/5 - 6 > -4
x/5 > 2
x > 10