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Chapter 1: Problem 114

Combine like terms. $$ -9 x-13 x+7 $$

Short Answer

Expert verified
-22x + 7

Step by step solution

01

Identify Like Terms

Like terms are terms that contain the same variables raised to the same power. In the expression o -9x - 13x + 7the like terms are -9x and -13x. The constant term + 7 is not like the others since it does not contain a variable.
02

Combine Like Terms

To combine like terms, add or subtract their coefficients. Combine -9x and -13x :o -9x - 13x = (-9 - 13)xo -22x
03

Write the Final Expression

After combining the like terms, rewrite the expression: -22x + 7

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Key Concepts

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

Algebraic Expressions
Algebraic expressions are combinations of variables, numbers, and operations. They can include addition, subtraction, multiplication, and division. In most cases, algebraic expressions do not have an equal sign. For example, the given expression -9x - 13x + 7 is an algebraic expression. It includes variables ( x ), numbers (-9, -13), and mathematical operations (- and +). Understanding algebraic expressions is important because they form the foundation of many algebra problems. They allow us to describe relationships mathematically and solve for unknowns.
Coefficients
Coefficients are the numerical parts of terms that contain variables. In the expression -9x - 13x + 7, the coefficients are -9 and -13, which are attached to the variable x . Coefficients tell us how many times the variable is being multiplied. When combining like terms, add or subtract their coefficients. For example, in the term -9x - 13x, we combine -9 and -13 to get -22. Therefore, the combined term is -22x. Identifying and combining coefficients correctly is key to simplifying expressions.
Constant Terms
Constant terms are the numbers in an algebraic expression that do not have variables attached. In the expression -9x - 13x + 7, the constant term is 7. Constant terms remain the same because they are not affected by the variables. When simplifying an expression, treat constant terms separately. For example, in this exercise, 7 is simply left as it is because there are no other constant terms to combine it with.
Like Terms
Like terms in an algebraic expression have the same variables raised to the same power. In the expression -9x - 13x+7 , the like terms are -9x and -13x . Both terms contain the variable x raised to the same power. To simplify expressions, you need to combine like terms by adding or subtracting their coefficients. Here, we combined -9x and -13x to get -22x. Remember, only like terms can be combined; constant terms or terms with different variables cannot be combined with each other.

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Most popular questions from this chapter

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