/*! 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 7 Solve each linear equation. $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 7

Solve each linear equation. $$ -(w-12)=30 $$

Short Answer

Expert verified
w=-18.

Step by step solution

01

Distribute the Negative Sign

Start by distributing the negative sign across the parentheses: . This gives us .
02

Simplify the Expression

Now, simplify the left-hand side: . This leaves us with .
03

Solve for w

To isolate w, add 12 to both sides of the equation: . Simplifying this will give the solution to the equation.

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
In this problem, we use the distributive property to eliminate the parentheses. The distributive property states that for any expressions \(a\), \(b\), and \(c\), the equation \(a(b + c) = ab + ac\) holds true. In our exercise, we have a negative sign outside the parentheses, which can be considered as multiplying by \(-1\). To apply this:
  • Distribute the \(-1\) to both terms inside the parentheses:
    \(-1(w-12) = -1 \times w + -1 \times -12\)
  • This simplifies to \(-w + 12\).
Simplifying Expressions
Simplifying expressions is an important step in solving linear equations. After using the distributive property, the next step is to simplify further to make the equation cleaner and easier to work with. In our case, after distributing the negative sign:
  • We obtained \(-w + 12 = 30\).
  • At this point, make sure all like terms are combined if necessary. Here, there are no further like terms to combine, so the simplified equation remains as it is.
Isolating Variables
The ultimate goal is to solve for the variable \(w\). To achieve this, we need to isolate \(w\) on one side of the equation. Here鈥檚 how we do it:
  • We have \(-w + 12 = 30\).
  • Subtract 12 from both sides, resulting in \(-w = 30 - 12\).
  • This simplifies to \(-w = 18\).
Finally, to solve for \(w\), multiply both sides of the equation by \(-1\) to get:
  • \(w = -18\).

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 using a geometry formula. The width of the rectangle is 0.7 meters less than the length. The perimeter of a rectangle is 52.6 meters. Find the dimensions of the rectangle.

Solve. Two busses leave Billings at the same time. The Seattle bus heads west on I-90 at a speed of 73 miles per hour while the Chicago bus heads east at a speed of 79 miles an hour. How many hours will it take them to be 532 miles apart?

Solve each number word problem. The sum of two numbers is 20 . One number is four less than the other. Find the numbers.

Solve each inequality, graph the solution, and write the solution in interval notation. $$ -8<5 x+2 \leq-3 $$

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(4-7 x \geq-3\) or \(5(x-3)+8>3\)
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

Pure Maths

Read Explanation

Applied 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.