-2 <= a + 3 < 8
so with these, all we do is work on both sides at once. just like how when there is an equal sign, if you change something on one side, you do the same thing on the other, this is the same principle. if we change something in the center, we must do the same thing on both ends, if i do something on one end, i must do the same in the center and the other end and so on. the thing to look out for when dealing with inequalities are these:
- if we multiply by a negative number, we turn the signs around.
- if we take the inverse of everything, we must turn the signs around.
now to get to your question
-2 <= a + 3 < 8 ..........let's get a by itself. subtract 3 throughout the system
=> -2 - 3 <= a < 8 - 3
=> -5 <= a < 5
we wouldn't graph this as a two dimensional graph, but as a one-dimensional graph
basically we draw a number line, where a line on the number line represents a, and circles represent the end points f our solution. if we can be equal to a value, we shade the circle, if we can't, we leave it unshaded