Problem 53 Simplify each expression. $$ ... [FREE SOLUTION]

91影视

Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 1: Problem 53

Simplify each expression. $$ 1+7 x+11 x-1+5 x $$

Short Answer

Expert verified

The simplified expression is $23x$.

Step by step solution

Identify Like Terms

Examine the given expression: $1 + 7x + 11x - 1 + 5x$. Recognize that the terms can be categorized into constants and terms with the variable $x$.

Combine Like Terms - Constants

Combine the constant terms $1$ and $-1$. This results in $1 - 1 = 0$. So the updated expression is simply the remaining terms: $7x + 11x + 5x$.

Combine Like Terms - Variable Terms

Combine the $x$ terms: $7x + 11x + 5x$. Add the coefficients of $x$ together: $7 + 11 + 5 = 23$. This results in $23x$.

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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 1 + 7x + 11x - 1 + 5x, all terms that include an 'x' are like terms. They share the same variable 'x' and are raised to the same power (which is 1 in this case). Recognizing like terms is crucial because it allows us to simplify expressions by combining them. In simpler terms, you can think of like terms as similar items that can be grouped together.
For the given expression, the like terms involving 'x' are 7x, 11x, and 5x. By adding these together, you combine their coefficients (numbers in front of the variables) into one single term.

Constants

Constants are the numbers in an expression that do not change because they do not have variables attached to them. In the expression 1 + 7x + 11x - 1 + 5x, the constants are 1 and -1. Since constants are just plain numbers, they can be added or subtracted without any complicated steps.
In our example, we add the constants 1 and -1, which equals 0. This part of the expression essentially cancels out, simplifying our work. So after combining the constants, what's left are just the variable terms involving 'x'.

Variable Terms

Variable terms have coefficients (numbers) and variables (like 'x'). In our example expression 1 + 7x + 11x - 1 + 5x, these are the terms with 'x'. When simplifying expressions, combine these variable terms by adding or subtracting their coefficients. This step involves basic addition or subtraction.
In the given problem, we identify the variable terms 7x, 11x, and 5x. To simplify, add their coefficients: 7 + 11 + 5. This results in 23x. Therefore, the final simplified expression is 23x.
Understanding how to handle variable terms is key to mastering algebraic expressions. It helps in further complex problem-solving, ensuring you work with the simplest form of an expression.

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91影视

Simplify each expression. $$ 1+7 x+11 x-1+5 x $$

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms - Constants

Combine Like Terms - Variable Terms

Key Concepts

Like Terms

Constants

Variable Terms

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