In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. −2≤x<5

Verified step by step guidance

1. Identify the given inequality system: \( -2 \leq x < 5 \). This describes all values of \( x \) that are greater than or equal to \( -2 \) and less than \( 5 \).
2. Understand that this is a one-variable inequality describing an interval on the number line, not a system involving \( y \) or other variables.
3. To graph this, draw a number line and mark the points \( -2 \) and \( 5 \).
4. At \( -2 \), use a closed circle or bracket to indicate that \( x \) can be equal to \( -2 \) (because of the \( \leq \) sign).
5. At \( 5 \), use an open circle or parenthesis to indicate that \( x \) cannot be equal to \( 5 \) (because of the \( < \) sign). Then shade the region on the number line between \( -2 \) and \( 5 \) to represent all values satisfying the inequality.

Key Concepts

Inequalities and Their Notation

Inequalities express a range of values that a variable can take, using symbols like ≤, <, ≥, and >. Understanding the difference between inclusive (≤, ≥) and exclusive (<, >) inequalities is essential for correctly interpreting the solution set.

Graphing Inequalities on the Number Line

Graphing inequalities involves shading the portion of the number line that satisfies the inequality. Closed dots represent inclusive boundaries (≤ or ≥), while open dots indicate exclusive boundaries (< or >). This visual helps identify all possible solutions.

Solution Sets of Systems of Inequalities

A system of inequalities requires finding values that satisfy all inequalities simultaneously. The solution set is the intersection of individual solution sets, which can be graphically represented to determine if solutions exist or if the system has no solution.