/*! 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 80 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 80

Simplify each expression. $$ 8.4(6 t-6)+2.4(9-3 t) $$

Short Answer

Expert verified
43.2t - 28.8

Step by step solution

01

- Distribute the Constants

Distribute the constant outside each parenthesis to each term inside the parenthesis.\[8.4(6t - 6) + 2.4(9 - 3t) = 8.4 \times 6t - 8.4 \times 6 + 2.4 \times 9 - 2.4 \times 3t\]\[= 50.4t - 50.4 + 21.6 - 7.2t\]
02

- Combine Like Terms

Combine the terms involving \(t\) and the constant terms separately.\[50.4t - 7.2t - 50.4 + 21.6\]Combine the coefficients of \(t\):\[50.4t - 7.2t = 43.2t\]Combine the constant terms:\[-50.4 + 21.6 = -28.8\]
03

- Write the Simplified Expression

Combine the simplified terms from Step 2 to form the final expression:\[43.2t - 28.8\]

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.

The Distributive Property
The Distributive Property is a fundamental concept in algebra. It's used to eliminate parentheses by distributing a factor across terms inside parentheses. For example, in the expression \(8.4(6t - 6) + 2.4(9 - 3t)\), the first step is to multiply each term inside the parentheses by the factor outside. This simplifies to \(8.4 \times 6t - 8.4 \times 6 + 2.4 \times 9 - 2.4 \times 3t\).
Distributing helps to make the expression easier to work with. Remember, each term inside the parentheses must be multiplied by the constant outside them. This calls for basic multiplication of each coefficient with the numbers inside the parentheses.
Combining Like Terms
After using the Distributive Property, the next step in simplifying an expression is to combine like terms. Like terms are terms that contain the same variables raised to the same power. For example, \(50.4t - 7.2t\) are like terms because they both contain the variable \(t\). Combining these gives us \(43.2t\).
Similarly, \(-50.4 + 21.6\) are constants (terms without variables) and should be combined as well. This simplifies to \(-28.8\).
When combining like terms, simply add or subtract their coefficients. This reduces the expression to its simplest form, making it easier to understand and use in further calculations.
Algebraic Simplification
The final step in our example is putting it all together into a simplified form. Algebraic simplification means to rewrite the expression in its most reduced form without changing its value.
From our previous steps, we've simplified the original expression \(8.4(6 t-6)+2.4(9-3 t)\) to \(43.2t - 28.8\). This final form is much simpler and more manageable.
Simplifying expressions helps to solve equations more efficiently and makes it easier to understand the relationships between variables. Always remember the key steps: distribute, combine like terms, and simplify.

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

give a number that satisfies the given condition. A whole number that is not positive and is less than 1

Simplify by finding the absolute value. $$ |6-3| $$

Insert one pair of parentheses so that the left side of each equation is equal to the right side. $$ 10-7-3=6 $$

Perform each indicated operation. $$ (5-12)(19-4) $$

Write each word phrase as an algebraic expression, using \(x\) as the variable. 18 divided by a number
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

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.