/*! 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 49 Add. $$(3 x+7)+(4 x-3)$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 49

Add. $$(3 x+7)+(4 x-3)$$

Short Answer

Expert verified
The simplified expression is \(7x+4\).

Step by step solution

01

Identifying Like Terms

The like terms in the given expression are \(3x\) and \(4x\), both of which contain the variable 'x'. Similarly, \(7\) and \(-3\) are like terms as they are both constants.
02

Combining Like Terms

Add \(3x\) and \(4x\) together to get \(7x\). Also, add \(7\) and \(-3\) together to get \(4\).
03

Writing the Simplified Expression

The simplified expression after combining like terms is \(7x+4\).

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.

Understanding Like Terms
In algebra, like terms are essential to simplify expressions. Like terms are terms that contain the same variable raised to the same power. For example, in the expression \(3x + 4x\), both \(3x\) and \(4x\) are like terms because they both contain the variable \(x\). Only the coefficients, which are the numbers in front of the variables, are different.
  • Variables must be identical to be considered like terms.
  • Constants, like \(7\) and \(-3\), are always like terms with one another because they don't contain any variables.
Recognizing like terms is the primary step in simplifying expressions because it helps in organizing and reducing complexity.
The Art of Combining Like Terms
Once you have identified like terms in an expression, the next step is combining them. Combining like terms involves adding or subtracting their coefficients while keeping the variable part unchanged.
  • With the terms \(3x\) and \(4x\), you simply add the coefficients: \(3 + 4\), which equals \(7x\).
  • For constants \(7\) and \(-3\), you perform simple arithmetic: \(7 - 3 = 4\).
By combining like terms, we condense the expression into a simpler form, making it easier to work with. This process is crucial for accurate manipulation in algebra problems.
Simplifying Expressions Made Easy
The final goal in algebraic operations like this one is to simplify expressions. Simplifying means transforming the original expression into its most streamlined form without changing its value.

To simplify, you:
  • Identify like terms and combine them as previously discussed.
  • Ensure all possible terms are merged.
  • Rewrite the expression neatly and clearly.
For the exercise \((3x + 7) + (4x - 3)\), after combining like terms, the resulting simplified expression is \(7x + 4\). Simplification is key to solving equations and understanding algebra deeply. It reduces complexity and sets the stage for advanced solutions.

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

Perform each division. Assume no division by \(0 .\) $$\frac{x^{3}+27}{x+3}$$

If \(f(x)=x^{2}-2 x+3,\) find each value. $$f(0.5)$$

Evaluate \(5 x-3\) for each value. $$x=-1$$

Writing the expression \((x+y)^{2}\) as \(x^{2}+y^{2}\) illustrates a common error. Explain.

Perform the operations. $$\begin{array}{r}-6 x^{3} z-4 x^{2} z^{2}+7 z^{3} \\\\+\quad-7 x^{3} z+9 x^{2} z^{2}-21 z^{3}\end{array}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

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.