/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 31 Simplify each algebraic expressi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 31

Simplify each algebraic expression by combining similar terms. $$9 x-14 x$$

Short Answer

Expert verified
The simplified expression is \(-5x\).

Step by step solution

01

Identify Similar Terms

The given algebraic expression is \( 9x - 14x \). Both terms are 'like terms' since they have the variable 'x.' Like terms have identical variable parts.
02

Combine the Coefficients

To simplify the expression, combine the coefficients of the like terms. The coefficients are 9 and -14. Perform the operation \(9 - 14 \).
03

Simplify the Expression

Subtract 14 from 9 to get the new coefficient: \(9 - 14 = -5\). Attach the common variable 'x' to the result, yielding the simplified expression \(-5x\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Combining Like Terms
Like terms are terms within an algebraic expression that have identical variable parts. This means that the same variable is raised to the same power. For example, in the expression \(9x - 14x\), both terms contain the variable \(x\), making them like terms.

Combining these like terms simplifies the expression, which reduces the number of terms and can make computations easier. To combine like terms, focus on their coefficients, because the variable part remains constant. This involves combining the numerical parts of each term, which will be explained further when discussing coefficients.
  • Identify terms that have the same variable and power.
  • Ensure all such terms are grouped together for simplification.
Coefficients
Understanding coefficients is crucial when working with algebraic expressions. A coefficient is the numerical factor in front of a variable in a term. In the expression \(9x - 14x\), 9 and -14 are the coefficients. These coefficients tell us how many times the variable part (in this case \(x\)) is taken.

To simplify an expression by combining like terms, focus on adding or subtracting these coefficients. This doesn't change the variable part but alters the expression's value.
  • Coefficients act as multipliers of their respective variable parts.
  • They must be combined according to the operation sign between them.
Simplification
Simplification in algebra means making an expression easier to understand or work with by combining like terms and other operations. It results in a neater, more concise form. Consider the expression \(9x - 14x\), where we've identified and combined the like terms. The coefficients, 9 and -14, when simplified, result in \(-5x\).

This new expression \(-5x\) is the simpler form of the original, stripped of any unnecessary complexity. This process makes equations more manageable and often easier to solve.
  • Follow a step-by-step approach: identify, combine, and simplify.
  • Always check that the simplified form accurately represents the original expression.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$(2)(-71)(50)$$

Simplify each algebraic expression by combining similar terms. $$12 x-14 x+x$$

Simplify each algebraic expression by combining similar terms. $$-2 x y+12+8 x y-16$$

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(8(x+4)-10(x-3)\) for \(x=-5\)

State the property that justifies each statement. For example, \(3+(-4)=(-4)+3\) because of the commutative property for addition. $$[6(-4)] 8=6[-4(8)]$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.