Compound inequalities

The  exercise appears under the Algebra I Math Mission. This exercise practices solving a compound inequality, i.e., satisfying more than one inequality simultaneously.

Types of Problems
There is one type of problem in this exercise:


 * 1) Solve the compound inequality: This problem provides two inequalities and a logical connector. The student is asked to select the option that corresponds to the correct solution of the compound inequality.Comine1.png

Strategies
Knowledge of the properties of inequality and comfort with the notation are needed to perform this exercise accurately and efficiently.
 * 1) Multiplying or dividing an inequality causes the inequality symbol to flip. This is because multiplying by a negative has the geometric effect of reflecting numbers on a one-dimensional number line over the origin.
 * 2) The connector AND means that both inequalities need to be true, the overlap or intersection of the two separate solutions.
 * 3) The connector OR means that either one or the other or both of the inequalities should hold, the union of the two separate solutions.
 * 4) The no solution option can only possibly happen on an AND problem, and the all real numbers option can only really happen on an OR.
 * 5) Often, but not all the time, the OR solution will be like wings and the AND solution will be an overlap segment in the graph on a number line.

Real-life Applications

 * 1) Inequalities are much more useful then equation in real-life because of the imprecise nature of the world. Good estimates become more powerful than exact answers.