/*! 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 58 Solve each equation. $$0.2 x-0... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 58

Solve each equation. $$0.2 x-0.05(x-100)=35$$

Short Answer

Expert verified
The solution to the equation is \(x = 200\).

Step by step solution

01

Distribute

Distribute the \[-0.05\] to both terms inside the parenthesis.\[0.2x - 0.05(x - 100) = 35\] becomes\[0.2x - 0.05x + 5 = 35\].
02

Combine like terms

Combine the terms involving \[x\] on the left-hand side.\[0.2x - 0.05x + 5 = 35\] becomes\[0.15x + 5 = 35\].
03

Isolate the variable term

Subtract 5 from both sides of the equation to isolate the term involving \[x\].\[0.15x + 5 - 5 = 35 - 5\] gives\[0.15x = 30\].
04

Solve for x

Divide both sides by \[0.15\] to solve for \[x\].\[x = \frac{30}{0.15}\] gives\[x = 200\].

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 is a fundamental concept in algebra. It allows you to multiply a single term by two or more terms inside a parenthesis.
For example, in the equation \(0.2x - 0.05(x - 100) = 35\), we need to distribute \(-0.05\) to both \(x\) and \(-100\).
This operation changes the equation to \(0.2x - 0.05x + 5 = 35\).
Applying the distributive property helps simplify equations, making it easier to solve them.
Combining Like Terms
Combining like terms involves simplifying an equation by adding or subtracting terms that contain the same variable.
In our example, after using the distributive property, we have \(0.2x - 0.05x + 5 = 35\).
Both \(0.2x\) and \(-0.05x\) are 'like terms'. By combining them, we get \(0.15x + 5 = 35\).
This step is crucial as it reduces the equation to a more manageable form, leading us closer to finding the solution.
Isolating the Variable
Isolating the variable means rearranging the equation so that the variable is by itself on one side of the equation.
In our problem, we have \(0.15x + 5 = 35\).
To isolate \(x\), we need to get rid of the constant term \(5\) on the left side. We do this by subtracting 5 from both sides, which gives us \(0.15x = 30\).
This step clears away every other term except the variable, making it easier to solve the equation.
Linear Equations
A linear equation is an equation that forms a straight line when graphed. It can be written in different forms, but the standard form is \(ax + b = c\).
Our example, \(0.2x - 0.05(x - 100) = 35\), may look complex, but it's just a linear equation.
By simplifying it using the distributive property, combining like terms, and isolating the variable, we can solve it.
Finally, we solve for \(x\) by dividing both sides by \(0.15\), giving us \(x = 200\).
This process shows how to handle linear equations step by step, ensuring we find the correct 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

Exploration a) Evaluate \(|m+n|\) and \(|m|+|n|\) for i) \(m=3\) and \(n=5\) ii) \(m=-3\) and \(n=5\) iii) \(m=3\) and \(n=-5\) iv) \(m=-3\) and \(n=-5\) b) What can you conclude about the relationship between \(|m+n|\) and \(|m|+|n| ?\)

Show a complete solution to each problem. Stacy's square. Stacy has 70 meters of fencing and plans to make a square pen. In one side she is going to leave an opening that is one-half the length of the side. If she uses all 70 meters of fencing, how large can the square be?

Show a complete solution to each problem. Tis the seasoning. Cheryl's Famous Pumpkin Pie Seasoning consists of a blend of cinnamon, nutmeg, and cloves. When Cheryl mixes up a batch, she uses 200 ounces of cinnamon, 100 ounces of nutmeg, and 100 ounces of cloves. If cinnamon sells for \(\$ 1.80\) per ounce, nutmeg sells for \(\$ 1.60\) per ounce, and cloves sell for \(\$ 1.40\) per ounce, what should be the price per ounce of the mixture?

Coast to coast. Sam and Dave are driving together across the United States. On the first day Sam averaged \(60 \mathrm{mph}\) and Dave averaged \(57 \mathrm{mph}\), but Sam drove for 3 hours less than Dave. If they drove a total of 873 miles that day, then for how many hours did Sam drive?

Solve problem by using an inequality. Car shopping. Jennifer is shopping for a new car. In addition to the price of the car, there is an \(8 \%\) sales tax and a \(\$ 172\) title and license fee. If Jennifer decides that she will spend less than \(\$ 10,000\) total, then what is the price range for the car?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

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.