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Chapter 2: Problem 29

In Exercises \(25-32\), simplify the expression by combining like terms. $$ 2 x+9 x+4 $$

Short Answer

Expert verified
So, the simplified form of the given expression '2x + 9x + 4' by combining like terms is '11x + 4'

Step by step solution

01

Identify Like Terms

Like terms are terms having the same variable with the same powers. Here, '2x' and '9x' are the like terms as they both are terms of 'x'.
02

Combine Like Terms

The next step is to add the coefficients of these like terms together. Coefficients are the numbers before the variables. For '2x' and '9x', coefficients are '2' and '9' respectively. Add these coefficients, so, \(2 + 9 = 11\), and then attach 'x' with this result to get '11x'.
03

Keep Other Terms

The term '4' is without any variable. Since there are no other plain numbers in the expression, it remains as '4'.
04

Final Simplified Expression

Now, combine '11x' and '4' to get the final simplified expression. It is written in the form of '11x + 4'.

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Key Concepts

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

Simplify Expression
When we talk about simplifying an expression in algebra, we refer to the process of making an equation or an expression easier to understand by combining like terms and eliminating unnecessary elements. Think of it as organizing a cluttered desk; you group similar items together to create an orderly and efficient workspace.
Like Terms
Like terms are the bread and butter of simplifying algebraic expressions. They are terms that share the same variable(s) raised to the same power. Imagine you have apples and oranges; you can only group apples with apples and oranges with oranges. In algebraic terms, this means that '3x' and '5x' can be combined because they both have 'x' as the variable, but '3x' cannot be combined with '3y' because the variables differ. Recognizing like terms is crucial because it's the first step in the process of simplification.
Coefficients
The term 'coefficient' refers to the number in front of the variable in an algebraic expression - think of it as a multiplier telling you how many times to count the variable. In the expression '5x', 5 is the coefficient, indicating that there are 5 'x's. When combining like terms, you add or subtract the coefficients while the variable remains unchanged.
Algebraic Expressions
Algebraic expressions are the phrases of the algebraic language. They consist of numbers, variables, and arithmetic operations such as addition and subtraction. A simple example is '4x + 5', where '4x' and '5' are terms of the expression. Algebraic expressions can be as simple or as complicated as a whole sentence or a long story. Simplifying these expressions, much like summarizing a story, makes them easier to work with and understand.

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Most popular questions from this chapter

In Exercises 33-38, justify each step of the equation. Then identify any properties of equality used to solve the equation. $$ \begin{aligned} 14-3 x &=5 \\ 14-3 x-14 &=5-14 \\ 14-14-3 x &=5-14 \\ -3 x &=-9 \\ \frac{-3 x}{-3} &=\frac{-9}{-3} \\ x &=3 \end{aligned} $$

In Exercises 27-32, solve the equation. $$ 3 x=30 $$

In Exercises \(1-10\), determine whether each value of \(x\) is a solution of the equation. \(2 x+5=-15\) (b) \(x=-10\) (b) \(x=5\)

In Exercises 79-84, evaluate the expression. $$ |4(-6)(5)| $$

In Exercises \(63-68\), simplify the expression. $$ \left(-3 y^{3}\right) y^{2} $$
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