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Definition

The symbol '>' is known as the 'greater than' sign, which is used to compare two values or expressions. When one quantity is greater than another, this symbol indicates that relationship, playing a crucial role in inequalities and absolute values. Understanding this concept is essential for solving problems that involve comparisons and for expressing solutions graphically on a number line.

5 Must Know Facts For Your Next Test

1. The symbol '>' is used to indicate that the value on the left side is larger than the value on the right side, such as in the expression '5 > 3'.
2. In solving inequalities, if you multiply or divide both sides by a negative number, you must flip the inequality sign.
3. When graphing an inequality with the '>' symbol, an open circle is placed on the number indicating that this value is not included in the solution set.
4. Inequalities can be combined using logical operators like 'and' and 'or' to form compound inequalities.
5. The solution to an inequality can often be expressed in interval notation, which indicates all numbers that satisfy the inequality.

Review Questions

• How can you apply the greater than sign to solve an inequality, and what are the implications of multiplying or dividing by a negative number?
  • To solve an inequality using the greater than sign, you isolate the variable on one side of the inequality. If you multiply or divide by a negative number during this process, you must flip the direction of the inequality sign. For example, in solving '-2x > 4', dividing by -2 would change it to 'x < -2'. This rule is crucial to maintain the correct relationship between the values being compared.
• What does it mean when you represent an inequality with a greater than sign on a number line?
  • When representing an inequality with a greater than sign on a number line, you place an open circle at the point corresponding to the value being compared, indicating that this point is not included in the solution set. For example, if you have 'x > 3', you would draw an open circle at 3 and shade to the right to show all numbers greater than 3 are part of the solution. This visual representation helps to easily identify all values that satisfy the inequality.
• Evaluate how inequalities involving the greater than sign can be manipulated to express solutions in interval notation and their significance in mathematics.
  • Inequalities involving the greater than sign can be manipulated algebraically to express solutions in interval notation, which is a concise way to describe sets of numbers. For instance, if you have 'x > 5', this can be expressed in interval notation as (5, ∞). The significance of interval notation lies in its ability to quickly convey ranges of solutions without listing every individual element. It also facilitates understanding complex inequalities and serves as a foundation for more advanced topics such as calculus and real analysis.

Related terms

Inequality: A mathematical statement that compares two expressions using signs like '>', '<', '≥', or '≤'.

Absolute Value: The distance of a number from zero on the number line, regardless of direction, often represented by the notation |x|.

Number Line: A visual representation of numbers arranged in order, where the position of each number corresponds to its value.