Identify the solution set of the inequality using the given replacement set. x < –4; {–5, –4.6, –4, –0.8, 1, 1.5}

The solution set is {-0.8, 1, 1.5}. You are just plugging in the values for x from the solution set. Then you see if it gives you a true mathematical statement. For example:

If you plug in -5 for x you get


which is not true, so it is not a solution. Therefore it is not apart of the solution set. Same for -4.6, and -4, as these values are not greater than -4. However when you substitute in -0.8 you get the solution:


which is true, and it is the same for 1 and 1.5, which is why these numbers would be considered as part of the solution set.