Match the inequality in each exercise in Column I with its equivalent interval notation in Column II . x≥-6

Verified step by step guidance

1. Identify the inequality given: \(x \geq -6\). This means \(x\) is greater than or equal to \(-6\).
2. Recall that interval notation uses brackets and parentheses to represent ranges of values. A square bracket \([\) or \(]\) means the endpoint is included (closed interval), while a parenthesis \((\) or \()\) means the endpoint is not included (open interval).
3. Since the inequality includes \(x \geq -6\), the number \(-6\) is included in the solution set, so we use a square bracket on the left side.
4. The inequality \(x \geq -6\) means \(x\) can be any number from \(-6\) up to positive infinity. Infinity is never included, so we use a parenthesis on the right side.
5. Write the interval notation as \([-6, \infty)\) to represent all \(x\) values greater than or equal to \(-6\).

Key Concepts

Inequalities and Their Symbols

Inequalities express the relationship between two values using symbols like ≥, ≤, >, and <. The symbol ≥ means 'greater than or equal to,' indicating all values greater than or exactly equal to a given number. Understanding these symbols is essential to translate inequalities into interval notation.

Interval Notation

Interval notation is a concise way to represent sets of numbers on the number line. It uses brackets [ ] to include endpoints and parentheses ( ) to exclude them. For example, x ≥ -6 corresponds to the interval [-6, ∞), including -6 and all numbers greater than it.

Matching Inequalities to Interval Notation

Matching involves identifying the correct interval notation that represents a given inequality. This requires understanding the inequality's direction and whether endpoints are included, then selecting the interval with appropriate brackets and bounds that reflect the inequality accurately.