/*! 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 Solve each equation. $$ 3 x+... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 81

Solve each equation. $$ 3 x+6=0 $$

Short Answer

Expert verified
x = -2

Step by step solution

01

Isolate the variable term

Subtract 6 from both sides of the equation to get:\[3x + 6 - 6 = 0 - 6\]This simplifies to:\[3x = -6\]
02

Solve for the variable

Divide both sides of the equation by 3 to solve for x:\[x = \frac{-6}{3}\]This simplifies to:\[x = -2\]

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.

isolate the variable
To solve a linear equation, the goal is to find the value of the unknown, often represented as \(x\). This process begins with 'isolating the variable.' First, you need to get the term with the variable \(x\) alone on one side of the equation.
In the exercise, the equation is: \(3x + 6 = 0\).
The term involving \(x\) is \(3x\).
Our aim is to isolate \(3x\) on one side. To do this, follow these steps.
subtracting from both sides
Next, you need to balance the equation by 'subtracting from both sides.'
Consider the equation from the exercise: \(3x + 6 = 0\). To isolate \(3x\), subtract 6 from both sides.

You will perform the operation: \(3x+6 - 6 = 0-6\). This simplifies to \(3x = -6\).
Remember,
  • If you add or subtract something on one side, you must add or subtract it on the other side too. This keeps the equation balanced.
  • This step ensures we move closer to isolating the variable.
dividing by a coefficient
Finally, start 'dividing by a coefficient' to solve for \(x\).
In the previous result, we have \(3x = -6\).
Here, 3 is the coefficient of \(x\). We need \(x\) alone, so divide both sides of the equation by 3.

Perform the operation: \(3x/3 = -6/3\). This simplifies to \(x = -2\).
  • Dividing both sides allows for \(x\) to be isolated.
  • This final step solves the equation, providing the value of the variable.

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 weight \(y\) (in pounds) of a man taller than 60 in. can be approximated by the linear equation \(y=5.5 x-220\) where \(x\) is the height of the man in inches. (a) Use the equation to approximate the weights of men whose heights are 62 in. 66 in. and 72 in. (b) Write the information from part (a) as three ordered pairs. (c) Graph the equation, using the data from part (b). (d) Use the graph to estimate the height of a man who weighs 155 lb. Then use the equation to find the height of this man to the nearst inch.

Describe what the graph of each linear equation will look like in the coordinate plane. (Hint: Rewrite the equation if necessary so that it is in a more recognizable form.) $$ x-10=1 $$

Solve each problem. As a fundraiser, a club is selling posters. The printer charges a \(\$ 25\) set- up fee, plus \(\$ 0.75\) for each poster. The cost \(y\) in dollars to print \(x\) posters is given by $$ y=0.75 x+25 $$ (a) What is the cost \(y\) in dollars to print 50 posters? To print 100 posters? (b) Find the number of posters \(x\) if the printer billed the club for costs of \(\$ 175 .\) (c) Write the information from parts (a) and (b) as three ordered pairs. (d) Use the data from part (c) to graph the equation.

Plot and label each point in a rectangular coordinate system. $$ (5,-4.25) $$

Solve each problem. It costs a flat fee of \(\$ 20\) plus \(\$ 5\) per day to rent a pressure washer. Therefore, the cost to rent the pressure washer for \(x\) days is given by $$ y=5 x+20 $$ where \(y\) is in dollars. Express each of the following as an ordered pair. (a) When the washer is rented for 5 days, the cost is \(\$ 45 .\) (b) I paid \(\$ 50\) when I returned the washer, so I must have rented it for 6 days.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.