Problem 65 - Intermediate Algebra

Question

Simplify by combining like terms. See Example 5 . $$0.7 h-3.8 h$$

Step-by-Step Solution

Answer

-3.1h

Step 1: Identify Like Terms

In the expression given, \(0.7h - 3.8h\), both terms contain the variable \(h\). This means they are like terms and can be combined.

Step 2: Combine Like Terms

To simplify the expression, we need to combine the coefficients of the like terms. Subtract \(3.8\) from \(0.7\): \(0.7 - 3.8 = -3.1\).

Step 3: Write the Simplified Expression

Now that we've combined the coefficients, we can write the simplified expression as \(-3.1h\).

Key Concepts

Combining Like Terms

Combining like terms is a key step in simplifying algebraic expressions. In an algebraic expression, like terms are terms that have the same variable raised to the same power. For example, in the expression \(0.7h - 3.8h\), both terms have the variable \(h\), making them like terms. This property allows us to combine these terms by adding or subtracting their coefficients.To simplify an expression using like terms, follow these steps:

• Identify all the like terms in your expression.
• Make sure their variables and their exponents are matched.
• Combine the coefficients of these terms appropriately.

This approach ensures that we can simplify expressions easily and accurately, essentially reducing the number of terms to a more manageable amount.

Coefficients

Coefficients are crucial parts of algebraic expressions. In algebra, the coefficient is the numerical part of a term that is multiplied by the variable. For instance, in the term \(0.7h\), the coefficient is \(0.7\). Similarly, in \(-3.8h\), the coefficient is \(-3.8\).Understanding coefficients is important because:

• They tell us the "amount" of the variable present in each term.
• They are the primary components we manipulate when combining like terms.

When simplifying expressions, you perform operations directly on the coefficients while keeping the variable part unchanged. This direct interaction with coefficients allows for a clear and efficient simplification process.

Simplification

Simplification in algebra refers to the process of transforming a complex expression into a simpler form. This makes it easier to work with while solving equations or performing further operations. By simplifying an expression, we reduce potential errors and enhance clarity.In the case of \(0.7h - 3.8h\), our goal was to turn this expression into the simplest possible form by performing these steps:

• Identifying and combining like terms, which reduces the expression's complexity.
• Calculating the result of the coefficients' operation, yielding a single term, \(-3.1h\).

The ultimate aim is to have fewer terms and simpler numerical coefficients, which in turn makes it easier to interpret and use the expression in further calculations.