Problem 23 - Algebra A Combined Function

Question

Rewrite each inequality so that the inequality symbol points in the opposite direction and the resulting statement has the same meaning as the given one. $$ 0<6 $$

Step-by-Step Solution

Answer

6 > 0

Step 1: Identify the Original Inequality

The original inequality given is \( 0 < 6 \). This inequality states that zero is less than six.

Step 2: Understand the Meaning

The inequality \( 0 < 6 \) tells us that zero is a smaller number compared to six. We need to keep this meaning when we flip the inequality symbol.

Step 3: Flip the Inequality Symbol

To rewrite the inequality with the symbol pointing in the opposite direction, we flip \( < \) to \( > \).

Step 4: Rewrite With Opposite Inequality

Write the inequality as \( 6 > 0 \). This reads as six is greater than zero, which maintains the same relationship as the original statement.

Key Concepts

Opposite Inequality

In algebra inequalities, an opposite inequality occurs when we change the direction of the inequality symbol. This means flipping the symbol itself. For example, if we start with the inequality "less than" (<), to write the opposite inequality, we change it to "greater than" (>). This doesn't alter the relationship between the two numbers or expressions involved, but simply expresses the same relationship in a different format. If you are given the inequality like 0 < 6, its opposite inequality would be 6 > 0. Both statements declare the same truth in a different way.

Inequality Symbols

Inequality symbols are a key part of understanding which way one value compares to another. These symbols include:

• "<" which stands for less than
• ">" which stands for greater than
• "≤" which stands for less than or equal to
• "≥" which stands for greater than or equal to

Each of these symbols helps to represent specific relationships between numbers or variables. Understanding which symbol to use is crucial in correctly expressing mathematical relationships.

Rewrite Inequality

Rewriting an inequality involves maintaining the truth of the original statement but changing its representation. For instance, with the inequality 0 < 6, rewriting it in its opposite form gives us 6 > 0. The key here is to ensure that the rewritten statement still conveys the same relationship and truth. We do this by adjusting the inequality symbol and swapping the positions of the numbers or expressions.

Inequality Meanings

Inequalities express how numbers or expressions compare to each other. For example, the inequality 0 < 6 indicates that zero is less than six. This is important for understanding number scales, ordering, and making comparisons. When dealing with inequalities, the meaning remains consistent even if the symbol direction changes, as long as the truth is preserved. So, 0 < 6 ("zero is less than six") maintains the same meaning as its counterpart 6 > 0 ("six is greater than zero"). Grasping these meanings helps in deciphering mathematical statements and problem-solving.