Problem 13 - Elementary and Intermediate Algebra

Question

Write each of the following in words. $$ -x-y $$

Step-by-Step Solution

Answer

negative x minus y

Step 1: Identify the terms

First, identify each term in the expression. In this case, the terms are \(-x\) and \(-y\).

Step 2: Determine the signs

Notice that both terms have a negative sign in front of them. This will affect how we write the phrase in words.

Step 3: Combine the terms in words

Combine both terms with appropriate wording. Since both terms are negative, we say 'negative x' and 'negative y'. After combining, the phrase becomes: 'negative x minus y'.

Key Concepts

Identifying Terms

In algebraic expressions, the first step is to **identify the terms**. Terms are the individual parts of an expression that are separated by addition or subtraction signs. For example, in the expression \(-x - y\), there are two terms: \(-x\) and \(-y\). Understanding terms is crucial because it helps us break down and simplify expressions effectively. This will also help in later steps, such as combining like terms or solving equations. Identifying terms correctly sets a strong foundation for more complex operations in algebra.

Negative Signs

Next, it's essential to **pay attention to negative signs** in algebraic expressions. Negative signs indicate that the value of the term is less than zero. In the expression \(-x - y\), both terms have negative signs in front of them. When reading or writing the expression in words, it's important to reflect these signs accurately. For example, \-x\ becomes 'negative x' and \-y\ becomes 'negative y'. This might seem simple, but it can get tricky in longer and more complex expressions, so practice is key. Recognizing negative signs helps ensure that we handle the values correctly in further mathematical operations.

Combining Terms

Lastly, we focus on **combining terms** to form a coherent phrase. After identifying the terms and their signs, we put them together in words. For the expression \(-x - y\), this means combining 'negative x' and 'negative y'. When combined, the phrase becomes 'negative x minus y'. Notice the word 'minus' here, which indicates subtraction between the terms. This step ensures that the expression is expressed clearly and accurately in words. Combining terms accurately is vital for clear communication, especially when sharing solutions with others or writing them out in descriptive forms.