Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. 6≤x

Verified step by step guidance

1. Identify the type of inequality given: \(6 \leq x\). This is a 'greater than or equal to' inequality.
2. Understand that \(x\) can be any number greater than or equal to 6.
3. In interval notation, a 'greater than or equal to' inequality is represented with a closed bracket on the side of the number it is equal to.
4. Since \(x\) can be any number from 6 to infinity, use a closed bracket for 6 and an open bracket for infinity.
5. Write the interval notation as \([6, \infty)\).

Key Concepts

Inequalities

Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They use symbols such as '≤' (less than or equal to) and '≥' (greater than or equal to) to indicate the range of values that satisfy the condition. Understanding how to interpret and manipulate inequalities is essential for solving problems that involve ranges of numbers.

Interval Notation

Interval notation is a mathematical notation used to represent a set of numbers between two endpoints. It uses brackets '[ ]' to include endpoints and parentheses '( )' to exclude them. For example, the interval [6, ∞) represents all numbers greater than or equal to 6. Familiarity with interval notation is crucial for translating inequalities into a concise format.

Graphing Inequalities

Graphing inequalities involves representing the solutions of an inequality on a number line. A solid dot is used for '≤' or '≥' to indicate that the endpoint is included, while an open dot is used for '<' or '>'. This visual representation helps in understanding the range of values that satisfy the inequality, making it easier to match with interval notation.