/*! 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 6 Simplify the given algebraic exp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 6

Simplify the given algebraic expressions. $$6 t-3 t-4 t$$

Short Answer

Expert verified
The simplified expression is \(-t\).

Step by step solution

01

Identify like terms

In the algebraic expression \(6t - 3t - 4t\), identify the like terms. All terms have the variable \(t\), so they can be combined.
02

Combine like terms

Combine the coefficients of the like terms, which are \(6\), \(-3\), and \(-4\). Add them together: \(6 - 3 - 4 = -1\).
03

Write the simplified expression

Multiply the combined coefficient \(-1\) by the variable \(t\) to form the simplified expression. Thus, the expression simplifies to \(-t\).

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.

Simplifying Expressions
In algebra, simplifying expressions means making them easier to understand or work with. This involves reducing the expression to its simplest form. The goal is to make calculations easier or to reveal the most important components of the expression. When we simplify, we look for ways to reduce complexity while maintaining the essence of the expression.

Here are some techniques we use to simplify algebraic expressions:
  • Identify and combine like terms to reduce the number of terms.
  • Apply the distributive property to expand or factor expressions.
  • Cancel common factors in fractions, if applicable.
Simplifying an expression helps us interpret results quickly and solve problems efficiently. It's like taking a cluttered room and organizing it neatly.
Like Terms
Like terms in algebra are terms that have identical variable parts. This means the variables in these terms are the same and raised to the same power. Only the coefficients might differ, which are the numerical values in front of the variables.

For example, in the expression:
  • \( 6t \) and \( -3t \) are like terms because they both contain the variable \( t \).
  • \( 4x^2 \) and \( 7x^2 \) are like terms because they share the variable \( x^2 \).
To simplify expressions, identifying like terms is essential because they allow you to combine them into a single term, making the overall expression easier to work with. Basically, it's like finding similar types of fruits in a basket and grouping them together.
Combining Coefficients
When you have identified like terms in an expression, the next step is to combine their coefficients. Coefficients are the numerical parts of terms and are multiplied by the variables in each term.

To combine coefficients:
  • First, ensure all terms you want to combine are indeed like terms, meaning they have identical variable parts.
  • Sum up (or subtract) the coefficients based on the operation present in the expression.
For example, in the expression \(6t - 3t - 4t\):
  • The coefficients are 6, -3, and -4.
  • Adding them gives: \( 6 - 3 - 4 = -1 \).
Finally, attach the resulting coefficient to the variable part: in this case, leading to \(-t\). By combining coefficients, you simplify and make the expression more straightforward. It's as if you are merging similar tasks into a single, more manageable task.

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 the given problems. A person \(1.8 \mathrm{m}\) tall is photographed with a \(35-\mathrm{mm}\) camera, and the film image is \(20 \mathrm{mm}\). Under the same conditions, how tall is a person whose film image is \(16 \mathrm{mm} ?\)

Perform the indicated divisions. In analyzing a rectangular computer image, the area and width of the image vary with time such that the length is given by the expression \(\frac{2 t^{3}+94 t^{2}-290 t+500}{2 t+100} .\) By performing the indicated division, find the expression for the length.

Solve the given problems. For what values of \(x\) is (a) \(x>\sqrt{x},\) (b) \(x=\sqrt{x}\), and (c) \(x<\sqrt{x} ?\)

Perform the indicated divisions. By division show that \(\frac{x^{5}+y^{3}}{x+y}\) is not equal to \(x^{2}+y^{2}.\)

Perform the indicated calculations. (a) Determine the number of seconds in a day in scientific notation. (b) Using the result of part (a), determine the number of seconds in a century (assume 365.24 days / year).
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

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.