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

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Identify the inequality given: \(x < -6\). This means all values of \(x\) are less than \(-6\).

Recall that interval notation expresses the set of all numbers satisfying the inequality using parentheses and brackets.

Since \(x\) is less than \(-6\) but does not include \(-6\), use a parenthesis to indicate that \(-6\) is not included: \((-\infty, -6)\).

The interval starts from negative infinity because there is no lower bound to the values \(x\) can take, and extends up to but not including \(-6\).

Therefore, the inequality \(x < -6\) corresponds to the interval notation \((-\infty, -6)\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Inequalities

Inequalities express a relationship where one quantity is less than or greater than another. In this case, x < -6 means all values of x are less than -6. Understanding how to interpret and manipulate inequalities is essential for solving and representing them.

Interval Notation

Interval notation is a concise way to represent sets of numbers between two endpoints. For inequalities like x < -6, the interval notation uses parentheses to indicate that -6 is not included, written as (-∞, -6). This notation helps clearly describe solution sets.

Matching Inequalities to Interval Notation

Matching involves translating an inequality into its equivalent interval form. Recognizing symbols like '<' or '≤' and knowing how they affect interval endpoints (open or closed) is crucial. This skill connects algebraic expressions with their set representations.