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Chapter 6: Problem 42

Simplify each algebraic expression. \(5 x+13 x\)

Short Answer

Expert verified
The simplified expression of the given problem \(5x + 13x\) is \(18x\).

Step by step solution

01

Understanding the problem

First, note that 5x and 13x are like terms as they both contain the variable 'x'. 'Like Terms' can be added or subtracted to simplify.
02

Combining like terms

Add the coefficients (numerical values) of the like terms: 5x and 13x. Add the numbers 5 and 13 to get the sum of 18.
03

Write the simplified term

The simplified version of the combined like terms should have the variable attached. So, the result would be 18x.

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Key Concepts

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

Understanding Like Terms
Like terms are terms in an algebraic expression that have exactly the same variable or variables, raised to the same power. They are essential when you are simplifying algebraic expressions.
For instance, in the expression \(5x + 13x\), both terms are considered like terms because they have the variable \(x\). Like terms can be combined by adding or subtracting their coefficients鈥攊n this case, the numbers before the variable.

When simplifying, always look for like terms to make your expression easier to work with. It鈥檚 like grouping apples with apples and oranges with oranges.
The Role of Variables
A variable is a symbol鈥攐ften a letter like \(x\), \(y\), or \(z\)鈥攖hat represents a number we don't know yet, or it can represent several numbers. Variables allow you to generalize math problems and create expressions that can be solved for different values.
In our example, \(x\) is the variable present in both terms \(5x\) and \(13x\). The variable remains unchanged when combining like terms.
  • The variable must be exactly the same across terms to be combined.
  • Variables are crucial for creating formulas and equations that can be applied in various situations.
By understanding variables, you can appreciate their flexibility and importance in algebra.
Deciphering Coefficients
Coefficients are the numerical part of the terms that are multiplied by the variable. They show how much of the variable you have.
In \(5x\) and \(13x\), the coefficients are 5 and 13, respectively. These numbers tell us how many times the variable \(x\) is being counted.

When simplifying expressions with like terms, you add or subtract their coefficients, but keep the variable the same.
  • Understanding coefficients helps in identifying like terms.
  • They help in adjusting the scale or size of the variable part of the term.
Properly managing coefficients is key to mastering the simplification of algebraic expressions.

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Most popular questions from this chapter

I solved \(-2 x+5 \geq 13\) and concluded that \(-4\) is the greatest integer in the solution set.

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