Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

When solving compound inequalities, what is the first step?

1. Combine the inequalities

2. Separate and solve each inequality

3. Ignore the inequalities

4. Graph the inequalities

The correct answer is: Separate and solve each inequality

When solving compound inequalities, the first step is to separate and solve each inequality. This means breaking down the compound inequality into its individual parts so that you can analyze and solve each one separately. For example, if you have an inequality like \(x - 3 < 2\) and \(x + 1 > 4\) combined into a compound statement, it’s crucial to isolate each inequality to find the values of \(x\) that satisfy both conditions. Once you have each part separated, you can methodically solve them, often leading to a solution set that you can later combine or graph based on the requirements of the problem. This separation ensures that you do not overlook any possible solutions or constraints that each inequality imposes on the variable. By addressing each inequality individually, you're establishing a clear pathway to understanding how they interact and what overall solutions they present when combined.