91Ó°ÊÓ

In mathematics, translating verbal expressions into inequalities is a crucial skill. It involves converting a statement or description in words into a mathematical inequality. To do this, we need to understand specific phrases and their mathematical counterparts.
For example, the phrase 'no less than' translates to '\textgreater or equal to (\textgreater=)'. So, if we say 'Angenita earns no less than \(12 per hour,' we are stating that her hourly earnings are at least \)12.
Translating verbal expressions helps set up a problem correctly for solving. It involves carefully reading the statement, identifying the mathematical operation or relationship, and then writing it down as an inequality.
The process usually includes:

• Reading the problem carefully.
• Identifying key phrases that indicate inequality.
• Using proper mathematical symbols to represent these phrases.

The symbol \textgreater or equal to (\textgreater=) is used in inequalities to express that a value is either greater than or exactly equal to another value. For example, if we say Angenita earns no less than \(12 per hour, it means her earnings per hour could be exactly \)12 or any amount greater than \(12.
This concept is widely used in various real-life situations, such as:

• Financial constraints: 'Spending must be no less than \)500' (\textgreater=$500).
• Performance metrics: 'Scores must be no less than 85 to pass' (\textgreater=85).

Understanding and correctly using \textgreater= helps in representing and solving real-world problems mathematically.

Defining variables is a fundamental step in setting up and solving any mathematical problem involving unknown quantities. A variable is a symbol, often a letter, that represents an unknown value in an equation or inequality.
In the example exercise, we defined the variable h to represent the number of dollars Angenita earns per hour. This step is essential because:

• It simplifies the expression and makes it more manageable.
• It gives us a clear starting point for writing the inequality.

When defining variables, it's important to choose meaningful symbols and clearly state what they represent. This helps avoid confusion and makes it easier to follow and solve the problem.