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Chapter 11: Problem 69

Collect like terms. $$ 2.7 x+2.3 y-1.9 x-1.8 y $$

Short Answer

Expert verified
0.8x + 0.5y

Step by step solution

01

Identify Like Terms

First, identify terms with the same variable. In the expression, the like terms are: terms with 'x' (i.e., 2.7x and -1.9x) and terms with 'y' (i.e., 2.3y and -1.8y).
02

Combine Like Terms with 'x'

Next, combine the coefficients of the terms with 'x': 2.7 and -1.9. This yields: 2.7x - 1.9x = (2.7 - 1.9)x = 0.8x.
03

Combine Like Terms with 'y'

Then, combine the coefficients of the terms with 'y': 2.3 and -1.8. This results in: 2.3y - 1.8y = (2.3 - 1.8)y = 0.5y.
04

Form the Simplified Expression

Combine the results of the like terms to form the simplified expression: 0.8x + 0.5y.

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Key Concepts

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

like terms
In algebra, 'like terms' are terms that have the same variable raised to the same power. For example, in the expression 2.7x + 2.3y - 1.9x - 1.8y, the terms 2.7x and -1.9x have the variable 'x' with the same power (which is 1). Likewise, 2.3y and -1.8y are also like terms because they share the same variable 'y' raised to the same power.

Identifying like terms is crucial when simplifying expressions because only like terms can be combined together. Without this identification, combining terms incorrectly will result in an invalid calculation. Look for terms with the same variable and same exponent 鈥� these will be your like terms.
combining coefficients
After identifying like terms, the next step is to combine their coefficients. The coefficient is the numerical part of the term. In our example expression:

2.7x + 2.3y - 1.9x - 1.8y,

the coefficient of 2.7x is 2.7, and the coefficient of -1.9x is -1.9.
Here is how we combine:
  • Combine the coefficients of x-term: \( 2.7 - 1.9 = 0.8 \)
  • Combine the coefficients of y-term: \( 2.3 - 1.8 = 0.5 \)

So, combining the coefficients of like terms means performing the arithmetic operations (addition or subtraction) on the numerical parts while keeping the variable part the same.
simplifying expressions
Simplifying expressions is the process of combining like terms and writing the expression in its simplest form. From the expression:
2.7x + 2.3y - 1.9x - 1.8y, we know the like terms are combined as: \( 0.8x + 0.5y \)
.

Here's why simplifying is important:
  • It makes the expression easier to understand
  • It highlights key relationships and patterns
  • It can be used for solving equations provides clear, concise results.
Simplifying may involve several steps, but ultimately it leads to a more manageable and interpretable mathematical expression. Always remember to look for like terms and combine their coefficients accurately.

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