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Chapter 2: Problem 112

Simplify by combining like terms whenever possible. $$0.18 x+0.25(72-x)$$

Short Answer

Expert verified
Combine like terms to get \[-0.07x + 18\]

Step by step solution

01

- Distribute the 0.25

First, apply the distributive property to the expression. This means multiplying 0.25 by each term inside the parentheses: \[0.25(72) - 0.25(x)\] Now we have: \[0.18x + 0.25 \times 72 - 0.25x\]
02

- Perform the Multiplication

Calculate the products from the distribution: \[0.18x + 18 - 0.25x\] This results from multiplying 0.25 by 72, which gives 18, and multiplying 0.25 by x, which gives 0.25x.
03

- Combine Like Terms

Combine the like terms, which are the terms with the variable x: \[0.18x - 0.25x + 18\] Perform the subtraction to obtain:\[-0.07x + 18\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

distributive property
The distributive property is a core concept in elementary algebra. It lets you multiply a number by a sum or difference inside parentheses. Here, we see how it's used to simplify expressions. Take the expression, $$0.18x + 0.25(72 - x)$$. Applying the distributive property, we multiply 0.25 by each term in the parentheses: $$0.25(72) - 0.25(x)$$.
This changes the original expression to: $$0.18x + 0.25 \times 72 - 0.25x$$.
Once you apply the distributive property correctly, you'll be left with a clearer and simpler expression to further simplify.
simplifying expressions
Simplifying expressions involves combining like terms and performing any operations to make the expression as simple as possible. For the expression $$0.18x + 0.25(72 - x)$$, our goal is to reduce it to its simplest form.
After applying the distributive property, we have: $$0.18x + 0.25 \times 72 - 0.25x$$.
We then perform the multiplication to find $$0.25 \times 72 = 18$$ and $$0.25 \times x = 0.25x$$. So, the expression becomes: $$0.18x + 18 - 0.25x$$.
Finally, to finish simplifying, we combine the like terms: $$0.18x$$ and $$-0.25x$$. This makes the expression: $$-0.07x + 18$$.
elementary algebra
Elementary algebra forms the foundation for all higher-level algebra studies. It includes basic operations like addition, subtraction, multiplication, and division involving variables and constants.
Understanding concepts like the distributive property and combining like terms is crucial in elementary algebra. In our example: $$0.18x + 0.25(72 - x)$$, first, the distributive property is used, and then, the like terms are combined.
These steps show how fundamental algebraic principles simplify complex expressions into simpler forms. The final expression, $$-0.07x + 18$$, looks much simpler and easier to understand.

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