/*! 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 813 Simplify using the distributive ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 813

Simplify using the distributive property. $$ 14(c-1)-8(c-6) $$

Short Answer

Expert verified
6c + 34

Step by step solution

01

Apply the distributive property to the first term

The distributive property states that \(a(b + c) = ab + ac\). Apply this to \(14(c - 1)\): \(14c - 14\).
02

Apply the distributive property to the second term

Now apply the distributive property to \(-8(c - 6)\): \ -8c + 48\.
03

Combine like terms

Add the results from Step 1 and Step 2: \(14c - 14 - 8c + 48\). Combine the like terms \(14c - 8c\) and \(-14 + 48\): \ 6c + 34 \.

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.

simplify algebraic expressions
Simplifying algebraic expressions is a fundamental skill in elementary algebra. It involves making an expression easier to understand and work with. This usually means reducing it to its most basic form. For example, when you simplify \[14(c - 1) - 8(c - 6)\], you follow a series of steps to rewrite the expression in a simpler way.

  • First, distribute the numbers outside the parentheses to each term inside the parentheses.
  • Then, combine like terms to reduce the expression to its simplest form.
By completing these steps, you transform a more complicated expression into something easier to manage and understand. This process helps you solve equations and understand the relationships between different algebraic expressions.
combine like terms
Combining like terms is another key concept in elementary algebra. Like terms are terms in an expression that have the same variables raised to the same power. For example, in the expression \(14c - 14 - 8c + 48\), the like terms include \(14c\) and \(-8c\), as well as the constants \(-14\) and \(48\).

  • First, identify the like terms in the expression.
  • Then, add or subtract the coefficients (numbers in front of the variables) of like terms.
In our example, we combine \(14c\) and \(-8c\) to get \(6c\). Similarly, combining \(-14\) and \(48\) gives us \(34\). So, \(14c - 14 - 8c + 48\) simplifies to \(6c + 34\). This makes the expression more straightforward and easier to work with for further computations or problem-solving.
elementary algebra
Elementary algebra is the foundation of all higher-level mathematics. It involves understanding and manipulating algebraic expressions and equations. Mastery of elementary algebra concepts such as the distributive property, combining like terms, and simplifying expressions is crucial for success in more advanced math courses.

Key topics in elementary algebra include:
  • The distributive property: Allows you to multiply a number by a group of numbers added together, as seen with \(14(c - 1)\) and \(-8(c - 6)\).
  • Combining like terms: Helps simplify expressions by adding or subtracting terms that have the same variables.
  • Simplifying expressions: Makes complex equations easier to understand and solve, providing a foundation for solving equations and inequalities.
By mastering these skills, you develop a strong mathematical foundation that will support your learning in both high school and college-level mathematics.

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

Convert the units. A killer whale weighs 4.6 tons. Convert the weight to pounds.

Solve. Renee attached a 6 feet 6 inch extension cord to her computer's 3 feet 8 inch power cord. What was the total length of the cords?

Simplify using the distributive property. $$ 9\left(\frac{5}{9} y-\frac{1}{3}\right) $$

Simplify using the distributive property. $$ 9(5 u+8)+2(u-6) $$

Simplify using the distributive property. $$ 10\left(\frac{3}{10} x-\frac{2}{5}\right) $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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.