/*! 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 86 \(4(k+6)-(8+3 k)=-5\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 86

\(4(k+6)-(8+3 k)=-5\)

Short Answer

Expert verified
k = -21

Step by step solution

01

Distribute in the Parentheses

Distribute the 4 into the parentheses: 4(k+6) becomes 4k + 24. The equation now is: 4k + 24 - (8 + 3k) = -5
02

Simplify the Equation

Distribute the negative sign to both 8 and 3k: The equation becomes: 4k + 24 - 8 - 3k = -5
03

Combine Like Terms

Combine the terms with k and the constant terms: 4k - 3k + 24 - 8 = -5 This simplifies to: k + 16 = -5
04

Isolate the Variable

Subtract 16 from both sides to isolate k: k = -5 - 16 This simplifies to: k = -21

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.

Distributive Property
The distributive property helps you to multiply a single term with each term inside the parentheses.
In our problem, we start with the equation: \[ 4(k+6) - (8 + 3k) = -5 \]
We need to distribute the 4 to both k and 6, so the equation becomes: \[ 4k + 24 - (8 + 3k) = -5 \]
This step is crucial because it helps to remove the parentheses and get closer to a simpler equation.
Combining Like Terms
After simplifying inside the parentheses, the next step is to combine like terms.
Starting from: \[ 4k + 24 - 8 - 3k = -5 \]
We need to merge all terms with k together and all constant terms together. The terms \( 4k \) and \( -3k \) combine to give: \[4k - 3k = k\]
The constants 24 and -8 combine to give: \[24 - 8 = 16\]
After combining these like terms, the equation simplifies to: \[ k + 16 = -5 \]
Isolating the Variable
To solve for k, we need to isolate it on one side of the equation.
The simplified equation is: \[ k + 16 = -5 \]
To isolate k, subtract 16 from both sides: \[ k + 16 - 16 = -5 - 16 \]
This further simplifies to: \[ k = -21 \]
By isolating k, we find the value of the variable.
Linear Equations
Linear equations are straightforward and involve variables with no exponents other than 1.
A typical linear equation looks like: \[ ax + b = c \]
Our problem can be classified as a linear equation because it follows this general form after simplifying using the distributive property and combining like terms.
To solve a linear equation:
  • Simplify using the distributive property if needed
  • Combine like terms
  • Isolate the variable

By following these steps, solving linear equations becomes a systematic process, making it easier to find the solution.

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

Find two consecutive odd integers such that 59 more than the lesser is four times the greater.

In the 2017 regular baseball season, the Cleveland Indians won 18 fewer than twice as many games as they lost. They played 162 regular-season games. How many wins and losses did the team have? (Data from www.MLB.com)

Norway earned 39 medals at the 2018 Winter Olympics. The number of gold medals earned was the same as the number of silver medals. The number of bronze medals earned was 3 fewer than the number of silver medals. How many of each kind of medal did Norway earn? (Data from The Gazette.)

Solve each equation for \(y\) $$ 5 x-y=2 $$

Find the measure of an angle such that the difference between the measures of its supplement and three times its complement is \(10^{\circ}\).
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.