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Chapter 1: Problem 93

Simplify each expression. $$ x-0.04(x+50) $$

Short Answer

Expert verified
0.96x - 2

Step by step solution

01

- Distribute the Multiplier

First, distribute the \(-0.04\) to both terms inside the parentheses \( (x+50) \). This means: \[ -0.04(x) + -0.04(50) \].
02

- Simplify the Products

Next, simplify the products: \( -0.04 \times x = -0.04x \) and \[ -0.04 \times 50 = -2 \].
03

- Combine Like Terms

Now combine the terms together: \( x - 0.04x - 2 \).
04

- Simplify the Expression

Finally, combine the like terms \( x - 0.04x \). This simplifies to: \[ 0.96x - 2 \].

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Key Concepts

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

Understanding the Distributive Property
The distributive property is a fundamental concept in algebra. It allows us to multiply a single term with each term inside a set of parentheses. In simpler words, if you have to multiply a number by a sum (or difference), you can distribute the multiplication to each addend first. For example, in the expression x - 0.04(x+50) , we apply the distributive property to -0.04(x+50) . This means we need to distribute -0.04 to both x and 50 inside the parentheses.
This step transforms our expression to -0.04(x) + -0.04(50) leading us to -0.04x - 2 .
Combining Like Terms
Like terms are terms that have the same variables and powers. Combining them simply means adding or subtracting the coefficients of these terms. This process helps simplify algebraic expressions.
In our example, after distributing -0.04 , we get the expression x - 0.04x - 2 . Here, x and -0.04x are like terms because they both contain x . To combine them, you subtract the coefficients (1 - 0.04) which gives you 0.96x .
So our expression simplifies from x - 0.04x - 2 to 0.96x -2 .
Final Algebraic Simplification
Algebraic simplification involves making an expression as simple as possible. Once all like terms are combined, and all possible operations have been performed, you've simplified the expression.
Taking our example from the previous steps: after combining x and -0.04x to get 0.96x , the expression is 0.96x - 2 . At this point, there are no more like terms to combine or operations to perform.
Therefore, 0.96x - 2 is the simplified version of the original expression x - 0.04(x + 50) .

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