Problem 43 Simplify. $$ (14 x-3 y)+(2 x... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 4: Problem 43

Simplify. $$ (14 x-3 y)+(2 x+3 y) $$

Short Answer

Expert verified

16x

Step by step solution

Identify Like Terms

Notice that there are two types of terms in the expression: terms involving $x$ and terms involving $y$. Group the $x$ terms together and the $y$ terms together.

Combine Like Terms

Add the coefficients of the $x$ terms: $14x + 2x = 16x$. Then combine the $y$ terms: $-3y + 3y = 0y$.

Simplify the Expression

Combine the results from Step 2: $16x + 0y = 16x$. Since \0y\ does not affect the sum, the simplified expression is \16x\.

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Key Concepts

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

like terms

Understanding 'like terms' is essential for simplifying algebraic expressions. Like terms have the same variable parts. This means the variables must be identical in both type and exponent. For example, in the given expression (14 x - 3 y) + (2 x + 3 y), '14x' and '2x' are like terms because both include the variable x raised to the same exponent. Similarly, '-3y' and '3y' are like terms because they both include the variable y. Identifying like terms allows you to group them together, simplifying the process of combining and reducing the equation.

combining terms

Once you've identified like terms, the next step is to combine them. Combining terms involves adding or subtracting their coefficients. In our exercise, we first group the x terms and the y terms: 14x + 2x and -3y + 3y. To combine these, simply add or subtract the coefficients:

For the x terms: 14x + 2x = 16x.
For the y terms: -3y + 3y = 0y.

Remember, when combining terms, only the coefficients (numbers in front of the variables) change. The variables themselves remain the same.

coefficients

Coefficients are the numerical part of the terms that multiply the variables. In the expression 14x - 3y + 2x + 3y, 14 and 2 are the coefficients of x, while -3 and 3 are the coefficients of y. When simplifying, you focus on adding or subtracting these coefficients. For instance:

Adding the coefficients of 14x and 2x gives you 16x.
Adding the coefficients of -3y and 3y results in 0y.

After combining terms, if a variable has a coefficient of zero (like 0y), it can be eliminated from the expression. Thus, 14x - 3y + 2x + 3y simplifies to 16x.

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91影视

Simplify. $$ (14 x-3 y)+(2 x+3 y) $$

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms

Simplify the Expression

Key Concepts

like terms

combining terms

coefficients

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