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Chapter 5: Problem 37

Combine like terms. $$ x+x+x+x+x $$

Short Answer

Expert verified
5x

Step by step solution

01

Identify the Terms

First, identify the terms in the expression. Here, the terms are all the same, which are five occurrences of the variable x.
02

Combine the Like Terms

Since all the terms are identical (x), add them together: \[ x + x + x + x + x = 5x \]

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Key Concepts

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

Algebra
Algebra is a branch of mathematics that uses symbols, typically letters, to represent numbers and quantities in formulas and equations. It's like a universal language for math. These symbols are called variables, and they make it easier to work with unknown values and relationships between numbers. In the given exercise, we're working with the variable 'x'. Algebra is fundamental as it lays the foundation for higher-level math and various fields like engineering, physics, and economics.
Simplifying Expressions
Simplifying expressions is about making math problems easier to handle. In our exercise, we鈥檙e combining like terms to simplify the expression. Like terms have the same variable raised to the same power. For example, in the expression \(x + x + x + x + x\), each term is \(x\). To simplify it, we count all the \(x\) terms: \(1, 2, 3, 4, 5\), and write it as \(5x\). This process reduces the complexity of equations, making them easier to solve and understand. Simplifying expressions is crucial because it helps you see the core structure of mathematical problems.
Basic Algebraic Operations
Basic algebraic operations include addition, subtraction, multiplication, and division of variables and constants. In our example, we're focusing on addition. When combining like terms, you essentially add their coefficients. Coefficients are the numbers in front of the variables. In the expression \(x + x + x + x + x\), the coefficients are all 1. Adding them together gives you \(1 + 1 + 1 + 1 + 1 = 5\). So, the simplified term is \(5x\). Understanding these operations helps you manipulate and solve more complex algebraic equations in the future.
Variable Terms
Variable terms are components of algebraic expressions that include a variable. A variable is a symbol, usually a letter, that represents an unknown number. In the expression from our exercise, \(x\) is the variable term. When we talk about combining like terms, we're focused on these variables. The important thing to remember is that you can only combine terms with the same variable. In the expression \(x + x + x + x + x\), all the terms are \(x\), so they can be combined into \(5x\). This makes working with algebraic expressions much simpler.

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Most popular questions from this chapter

Add. $$ \begin{array}{c}{-6 y^{3}+8 y+5} \\ {9 y^{3}+4 y-6} \\ \hline\end{array} $$

Combine like terms. $$ 6 m^{2} n-8 m n^{2}+3 m n^{2}-7 m^{2} n $$

Find each product. $$ 5 y(-6 y+1) $$

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ \left(\frac{7 m^{-2}}{m^{-3}}\right)^{-2} \cdot \frac{m^{3}}{4} $$

Write each number in standard notation. $$ 7.2 \times 10^{4} $$
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