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Chapter 2: Problem 100

Simplify by combining like terms whenever possible. $$0.085 x+28.75+0.072 x+54.8$$

Short Answer

Expert verified
0.157x + 83.55

Step by step solution

01

- Identify like terms

Look at the given expression: 0.085x + 28.75 + 0.072x + 54.8Identify terms with the same variables (like terms). Here, 0.085x and 0.072x are like terms, and 28.75 and 54.8 are constants.
02

- Combine the like terms with the variable x

Add the coefficients of the like terms with the variable x: 0.085x + 0.072x = 0.157x
03

- Add the constant terms

Add the constant terms together: 28.75 + 54.8 = 83.55
04

- Write the simplified expression

Combine the results from step 2 and step 3 to get the simplified expression: 0.157x + 83.55

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Key Concepts

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

simplifying algebraic expressions
Simplifying algebraic expressions involves making an expression easier to work with by combining like terms and performing basic arithmetic operations.
Let's take the expression from the exercise: 0.085x + 28.75 + 0.072x + 54.8.

Start by identifying the like terms. In this example, the terms 0.085x and 0.072x both contain the variable x. The constants are 28.75 and 54.8.
Combining these like terms simplifies the expression, reducing it to fewer, more manageable terms.

like terms
Like terms are terms that have identical variables raised to the same power. This means that the coefficients can be different, but the variable parts must be the same.

In our example, 0.085x and 0.072x are like terms because both include the variable x with the same exponent (implicitly 1).
On the other hand, 28.75 and 54.8 are like terms because they are both constants (zero power of any variable).

To combine like terms, simply add or subtract their coefficients. This helps to simplify the expression accurately.
coefficients
Coefficients are the numerical parts of the terms that multiply the variable. In the term 0.085x, 0.085 is the coefficient.

Similarly, in 0.072x, 0.072 is the coefficient. When combining like terms, add the coefficients of the terms with the same variables.

For instance, adding the coefficients 0.085 and 0.072 gives us 0.157. Hence, 0.085x + 0.072x simplifies to 0.157x.
Understanding coefficients is essential for combining and simplifying like terms properly.
constants
Constants are the terms in algebraic expressions that do not contain any variables. They remain unaffected by the values of the variables.

In our example, the constants are 28.75 and 54.8.
To simplify the expression, simply add these constants together:
28.75 + 54.8 = 83.55.

Identifying and combining constants helps to reduce the expression to its simplest form.
Thus, the final simplified expression is 0.157x + 83.55.

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