/*! 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 35 Simplify. $$ 2 x-3 x $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 35

Simplify. $$ 2 x-3 x $$

Short Answer

Expert verified
-x

Step by step solution

01

Combine Like Terms

The expression given is \(2x - 3x\). Both terms are 'like terms' because they are multiples of \(x\). The expression can be combined by subtracting the coefficients of \(x\). This means we perform the operation \(2 - 3\), which results in \(-1\).
02

Write the Simplified Expression

After finding the coefficient by summing \(2 - 3 = -1\), the simplified expression becomes \(-1x\). In standard form, it is usually written as \(-x\). Thus, \(2x - 3x = -x\).

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.

Like Terms
In algebra, 'like terms' are terms that contain the same variable raised to the same power. Identifying like terms is crucial for simplifying expressions, as it allows us to combine them effectively. For instance, consider the expression \(2x - 3x\). Here, both terms contain the variable \(x\) with the same power, which makes them like terms. Thus, they can be joined together by operating on their coefficients.
  • Like terms must have identical variables and exponents.
  • Example: \(5y\) and \(-2y\) are like terms, but \(5y^2\) and \(5y\) are not.
  • Identifying like terms makes algebraic simplification easier.
Recognizing like terms is the first step to efficiently simplifying algebraic expressions.
Coefficients
The concept of 'coefficients' is foundational in algebra. A coefficient is a number that multiplies a variable in an algebraic expression. In the expression \(2x - 3x\), the numbers 2 and -3 are coefficients. They indicate how many times the variable \(x\) is taken into account.
  • A coefficient is often an integer but can also be a fraction or decimal.
  • The expression \(a \cdot b\) has 'a' as the coefficient of 'b'.
When combining like terms, we focus on adding or subtracting the coefficients. This step leads us towards simplifying the whole expression. In our example, performing \(2 - 3\) gives us the combined coefficient of \(-1\) for \(x\). Thus, understanding coefficients allows us to restructure and simplify expressions effectively.
Algebraic Simplification
Algebraic simplification is the process of reducing an expression to its simplest form. In this context, simplifying involves combining like terms and optimizing the way terms in an expression are represented. For \(2x - 3x\), simplifying means performing the math on the coefficients to combine the terms effectively.
  • Start by identifying like terms within the expression.
  • Operate on the coefficients of the like terms.
  • Rewrite the expression using the newly found coefficients.
In our example, subtracting the coefficients, \(2 - 3 = -1\), gives us the simplified term \(-x\). Doing so helps in making the expression more manageable and understandable.By comprehensively simplifying algebraic expressions, you create versions that are easier to interpret and utilize in predictions or problem-solving.

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

Solve and graph the solution set. In addition, present the solution set in interval notation. $$ 3 x \leq-15 \text { or } 2 x>6 $$

A recipe calls for \(11 / 2\) teaspoons of vanilla extract for every 3 cups of batter. How many teaspoons of vanilla extract should be used with 7 cups of batter?

At the same time of day, a pole casts a 27-foot shadow and 4-foot boy casts a 6-foot shadow. Calculate the height of the pole.

Solve and graph the solution set. In addition, present the solution set in interval notation. $$ -15 \leq 23 x-15<45 $$

If triangle \(A B C\) is similar to triangle RST, then find the remaining two sides given the following. \(a=4, b=9, c=12,\) and \(s=3\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.