/*! 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 81 Use the distributive property to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 81

Use the distributive property to rewrite each expression. $$ -3(2 x-5) $$

Short Answer

Expert verified
-6x + 15

Step by step solution

01

Identify the Distributive Property

The distributive property states that for any numbers, a, b, and c, the expression: \[ a(b + c) = ab + ac \] or \[ a(b - c) = ab - ac \]
02

Apply the Distributive Property

In this problem, the expression is \(-3(2x - 5)\). Here, \(a = -3\), \(b = 2x\), and \(c = 5\). Applying the distributive property gives: \[ -3(2x - 5) = -3 \times 2x - (-3) \times 5 \]
03

Simplify the Expression

Multiply the terms: \[ -3 \times 2x = -6x \] and \[ -(-3) \times 5 = 15 \] Therefore, the expression simplifies to: \[ -3(2x - 5) = -6x + 15 \]

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.

algebraic expressions
An algebraic expression includes numbers, variables, and arithmetic operations combined together. Variables are symbols that represent unknown values, typically shown as letters like x, y, or z. These expressions help us describe relationships and solve various problems in algebra.
Examples of algebraic expressions are:
  • 3x + 2
  • 7y - 4
  • 2a^2 + 3a - 1
In the exercise given,
we need to understand each part of the expression. For instance, -3(2x - 5) includes:
  • Coefficient: -3
  • Variable: x
  • Constant: -5
Understanding how to manipulate and simplify these expressions is key to solving algebraic problems.
simplifying expressions
Simplifying expressions means making them easier to work with by combining like terms, using properties such as the distributive property, and performing arithmetic operations. The goal is to rewrite the expression in its most simplified form.
Consider the expression we are given:
  • -3(2x - 5)
By applying the distributive property, we can break down the expression into simpler parts:
  • First, distribute -3 to both 2x and -5
  • Then, perform the multiplication
  • Combine the results to create a new, simpler expression
The result is:
-3(2x - 5) = -6x + 15
Steps to simplify:
  • Distribute: -3 * 2x = -6x
  • Distribute: -3 * (-5) = 15
  • Combine: -6x + 15
Through simplification, the expression is now easier to interpret and use in further calculations.
multiplication in algebra
Multiplication in algebra extends the basic concept of multiplication to include variables and constants. Multiplication can be between:
  • Two constants: 3 * 2 = 6
  • Constant and variable: 3 * x = 3x
  • Two variables: x * y = xy
In our exercise, we've applied multiplication within the distributive property. Here's a closer look:
Given: -3(2x - 5)
  • Multiply -3 by 2x: -3 * 2x = -6x
  • Multiply -3 by -5: -3 * (-5) = 15
This shows how multiplication distributes over addition and subtraction. The distributive property states that:
a(b + c) = ab + ac
In essence, we multiply each term inside the parentheses by the term outside. Understanding and mastering multiplication with variables helps you tackle more complex algebraic expressions.

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 each problem. The lowest temperature ever recorded in Arkansas was \(-29^{\circ} \mathrm{F}\). The highest temperature ever recorded there was \(149^{\circ} \mathrm{F}\) more than the lowest. What was this highest temperature? (Data from National Climatic Data Center.)

Solve each problem. Marcial owes \(\$ 679.00\) on his Visa account. He returns three items costing \(\$ 36.89, \$ 29.40\), and \(\$ 113.55\) and receives credit for these on the account. Next, he makes purchases of \(\$ 135.78\) and \(\$ 412.88\) and two purchases of \(\$ 20.00\) each. He makes a payment of \(\$ 400\). He then incurs a finance charge of \(\$ 24.57 .\) How much does he still owe?

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(6 x-5 y+4 a\)

Write a numerical expression for each phrase, and simplify the expression. The sum of \(\frac{3}{4}\) and \(\frac{1}{2},\) times the difference of \(\frac{2}{3}\) and \(\frac{1}{6}\)

Solve each problem. In September, Jeffery began with a checking account balance of \(\$ 537.12 .\) He made the following withdrawals and deposits. $$ \begin{array}{|c|c|} \hline \text { Withdrawals } & \text { Deposits } \\ \hline \$ 41.29 & \$ 80.59 \\ \$ 13.66 & \$ 276.13 \\ \$ 84.40 & \\ \hline \end{array} $$ Assuming no other transactions, what was his new account balance?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

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.