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In algebra, variables play a crucial role by acting as placeholders for unknown values in mathematical expressions and equations. They are often represented by letters such as \( x \), \( y \), or \( z \).

These symbols allow mathematicians and students to work with general concepts and solve problems without focusing on specific numbers initially. For example, in the exercise we're considering here, the phrase "a number" refers to an unknown value. We represent this unknown with a variable, such as \( x \).

By using variables, we have the flexibility to substitute any number into our expression later on.

Variables offer many benefits:

• They make it easy to express a wide range of problems with a simple formula.
• They allow generalization, which helps in solving varied problems without changing the framework.
• They enable us to understand the relationship between different quantities.

Translation of phrases in mathematics involves converting verbal expressions into algebraic expressions. This is an essential skill in algebra as it forms the foundation for understanding and solving word problems.

Breaking down a sentence or phrase into mathematical terms requires practice and understanding of key terms.

For the exercise provided, the phrase "decreased by a number" is central. Here are some basic tips for translating such phrases:

• "Decreased by" usually signals that subtraction is involved.
• "A number" typically refers to a variable that represents an unknown quantity.

You then combine these insights to build the corresponding algebraic expression. In our case, the initial value of \(-5 \frac{2}{7}\) is decreased by a variable \( x \). So, the translation results in \(-5 \frac{2}{7} - x\).
Try practicing with different phrases to strengthen this vital skill.

Subtraction in algebra functions much like arithmetic subtraction, but with the inclusion of variables.

To "subtract one quantity from another," you place the quantity being subtracted after the subtraction operator ("-"). The phrase from the exercise, "decreased by," requires you to subtract the variable \( x \) from the constant \(-5 \frac{2}{7}\). Thus, it becomes \(-5 \frac{2}{7} - x\).

Here are a few tips to keep in mind regarding subtraction in algebra:

• The order of terms matters in subtraction; reversing the terms changes the result.
• Always perform operations carefully, especially when negative numbers and variables are involved.
• Write expressions clearly and simplify them when possible.

Understanding subtraction in an algebraic context is vital since solving equations often involves adding and subtracting terms to isolate variables or achieve desired forms.