Denote this idea with an open dot on the number line and a round parenthesis in interval notation.
The number on the right should be greater than the number on the left. You will use the same properties to solve compound inequalities that you used to solve regular inequalities. Combine the solutions.
To express the solution graphically, draw a number line and shade in all the values that are solutions to the inequality. If the solution set were all numbers between -2 and 3, including -2 and 3, the solution set would be written as: [-2,3].
Since the word and joins the two inequalities, the solution is the overlap of the two solutions. Graphing the inequality helps with this interpretation.
Apparently Cecilia has both of these qualities; therefore she is the intersection of the two. This is what we call a union, as mentioned above.
Note how each inequality is treated independently until the end where the solution is described in terms of both inequalities.
In words, x must be less than 6 and at the same time, it must be greater than 2, much like the Venn diagram above, where Cecilia is at once breaking your heart and shaking your confidence daily. Switch the inequality if you multiply or divide by a negative number. In this case, we have less than or equal to zero, so we want the negative section.
The next example involves dividing by a negative to isolate a variable.