/*! 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 Solve each equation, and check t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 80

Solve each equation, and check the solution. $$ -6(4 x+3)+18=-48 $$

Short Answer

Expert verified
The solution is x = 2.

Step by step solution

01

Distribute the -6

Apply the distributive property by multiplying -6 with both terms inside the parentheses: o -6(4x + 3) + 18 = -48o -24x - 18 + 18 = -48
02

Simplify the equation

Combine like terms on the left side: o -24x - 18 + 18 = -48 o -24x = -48
03

Solve for x

Divide both sides of the equation by -24 to isolate x: o -24x / -24 = -48 / -24 o x = 2
04

Check the solution

Substitute x = 2 back into the original equation to verify the solution: o -6(4(2) + 3) + 18 = -48 o -6(8 + 3) + 18 = -48 o -6(11) + 18 = -48 o -66 + 18 = -48 o -48 = -48 Since both sides of the equation are equal, x = 2 is the correct solution.

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.

Applying the Distributive Property
The distributive property is a fundamental principle used in algebra to simplify equations. In our given problem, we apply this property to the expression \(-6(4x + 3) + 18 = -48\). These steps break down as follows:
  • Multiply -6 with 4x to get -24x, and
  • Multiply -6 with 3 to get -18.
This changes the equation into \(-24x - 18 + 18 = -48\). The distributive property helps to eliminate parentheses, making the equation easier to solve.
Combining Like Terms
After using the distributive property, the next step is to simplify the equation by combining like terms. Like terms are terms that have the same variable raised to the same power. In this case, you have:
  • \-24x\ (a term with a variable) and
  • \-18 \and \+18\ (constants).
On the left side of the equation, \(-24x - 18 + 18 = -48\), the -18 and +18 cancel each other out, simplifying our equation to \(-24x = -48\). Combining like terms helps us to reduce complex equations to simpler ones.
Isolating the Variable
Once the equation is simplified, the next critical step is to isolate the variable (in this case, x). To isolate x, we need to get x by itself on one side of the equation. Here, it involves dividing both sides by -24:
  • \-24x / -24 = -48 / -24\.
This division results in \(x = 2\). Isolating variables is crucial for solving most algebraic equations, allowing us to find the value of the unknown.
Checking the Solutions
After isolating the variable and solving the equation, it is always essential to verify the solution. This ensures our solution is correct. In our case, substitute \(x = 2\) back into the original equation:
\(-6(4(2) + 3) + 18 = -48\)
  • Calculate the inner expression, \(4(2) + 3 = 11\),
  • then multiply by -6, producing \(-6(11) = -66\), and
  • finally, add 18 to get \(-66 + 18 = -48\).
Since both sides of the equation are equal (\tilde \(-48 = -48\)), our solution for \(x = 2\) is verified and correct. Checking solutions helps confirm our calculations and identifies any potential errors.

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 even integers such that six times the lesser added to the greater gives a sum of 86 .

Find two consecutive even integers such that the lesser added to three times the greater gives a sum of \(46 .\)

Solve each formula for the specified variable. \(A x+B y=C\) for \(y\)

The world's largest taco contained approximately \(1 \mathrm{~kg}\) of onion for every \(6.6 \mathrm{~kg}\) of grilled steak. The total weight of these two ingredients was \(617.6 \mathrm{~kg}\). To the nearest tenth of a kilogram, how many kilograms of each ingredient were used to make the taco? (Data from Guinness World Records.

Graph the solution set, and write it using interval notation \(-6 \leq \frac{1}{3} x+3 \leq 5\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.