/*! 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 8 Combine like terms and simplify.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 8

Combine like terms and simplify. $$-7 x-3 x-1+9 x+6-2 x$$

Short Answer

Expert verified
The simplified form of the given expression is \(-2x + 5\).

Step by step solution

01

Identify like terms

In the given expression \(-7x -3x -1+9x+6-2x\), we have the following like terms: 1. Terms with x: \(-7x, -3x, 9x, -2x\) 2. Constant terms: \(-1, 6\)
02

Combine terms with x

To combine the terms with x, add the coefficients of all the terms: \((-7) +(-3) +9 +(-2) = -7 -3 +9 -2 = -2x\)
03

Combine constant terms

Now combine the constant terms, -1 and 6: \(-1 +6 = 5\)
04

Write the final simplified expression

After combining like terms, we get the expression: \(-2x + 5\) The simplified form of the given expression is \(-2x + 5\).

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
To simplify an expression, the first step is to "combine like terms." But what does that mean? "Like terms" are terms that have the same variable raised to the same power. In other words, they are similar! For example, in the expression \(-7x -3x -1+9x+6-2x\), you can see several "like terms."
  • The terms \(-7x, -3x, 9x,\) and \(-2x\) are like terms because they all contain the variable \(x\).
  • The numbers \(-1\) and \(6\) are also like terms, known as constant terms, because they are just plain numbers without variables.
Combining like terms involves adding or subtracting the coefficients (the numbers in front of the variables) to form one term. This process helps simplify the equation and makes it easier to solve or evaluate further.
Simplifying Expressions
Once you've combined like terms, the next step is "simplifying expressions." Simplifying means making the expression as straightforward as possible by performing all possible operations.
In the original exercise, after combining like terms, we simplify the expression:
  • For the \(x\) terms: We had \((-7) + (-3) + 9 + (-2) = -2\). So, the \(x\) terms are consolidated to \(-2x\).
  • For the constants: We combine \(-1 + 6 = 5\).
Putting it all together, the simplified expression is \(-2x + 5\). Simplifying expressions is powerful because it reduces complex problems into simpler, more manageable forms.
Algebraic Expressions
"Algebraic expressions" are mathematical phrases that can include numbers, variables, and operators. Consider the expression provided: \(-7x -3x -1+9x+6-2x\). It combines several elements:
  • Variables, like \(x\), represent unknown or variable quantities.
  • Coefficients, such as \(-7\), \(-3\), \(9\), and \(-2\), are the numbers multiplied by the variables.
  • Constants, like \(-1\) and \(6\), are standalone numbers.
  • Operators, including addition \((+)\) and subtraction \((-)\), connect the various terms.
Algebraic expressions are the foundation of many mathematical computations and problems. They allow us to describe mathematical relationships flexibly and concisely, paving the way for solving equations and inequalities effectively.

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 using the quotient rule. $$\frac{-6 k}{k^{4}}$$

Simplify using the quotient rule. $$\frac{3 a^{2} b^{-5}}{15 a^{-8} b^{3}}$$

Simplify the expression using one of the power rules. $$\left(\frac{n}{5}\right)^{3}$$

Simplify using the quotient rule. $$\frac{21 t u^{-3}}{14 t^{7} u^{-9}}$$

Write each number in scientific notation. -0.00000022
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.