/*! 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 73 Solve each equation, and check t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 73

Solve each equation, and check the solution. \(0.05 x+0.12(x+5000)=940\)

Short Answer

Expert verified
The solution is \(x = 2000\).

Step by step solution

01

Distribute the Constants

Distribute the 0.12 across the terms inside the parentheses: \(0.12(x + 5000) = 0.12x + 600\). This gives the equation: \(0.05x + 0.12x + 600 = 940\).
02

Combine Like Terms

Combine the terms with \(x\): \(0.05x + 0.12x = 0.17x\). This updates our equation to: \(0.17x + 600 = 940\).
03

Isolate the Variable

Subtract 600 from both sides of the equation to isolate the term with \(x\): \(0.17x = 340\).
04

Solve for \(x\)

Divide both sides of the equation by 0.17 to solve for \(x\): \(x = \frac{340}{0.17} = 2000\). The solution is \(x = 2000\).
05

Check the Solution

Substitute \(x = 2000\) back into the original equation to verify: \(0.05(2000) + 0.12(2000 + 5000) = 100 + 0.12(7000) = 100 + 840 = 940\). The solution checks out correctly.

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 in algebra helps to simplify an equation by distributing multiplication over addition or subtraction within parentheses. In the equation provided, we have the term 0.12(x + 5000). To simplify this, you multiply 0.12 by each term inside the parentheses:

0.12(x) + 0.12(5000).

This gives us:

0.12x + 600.

Now the equation looks simpler and ready for the next steps: 0.05x + 0.12x + 600 = 940.
combining like terms
After using the distributive property, the next step is combining like terms. Like terms are terms that have the same variables raised to the same power. In our equation, we combined the terms that both have x:

0.05x and 0.12x.

When we add these coefficients together, we get:

0.05x + 0.12x = 0.17x.

So our equation becomes:

0.17x + 600 = 940.

This step simplifies our equation further and brings us closer to solving for x.
isolating variables
This step focuses on isolating the variable on one side of the equation to solve for it. In our simplified equation 0.17x + 600 = 940, we aim to isolate x. We do this by getting rid of the constant term (600) on the same side as the variable. Subtract 600 from both sides:

0.17x + 600 - 600 = 940 - 600.

This simplifies to:

0.17x = 340.

Now, x is almost isolated. The final step involves solving for x.
checking solutions
Once we find a solution, it's crucial to check it to ensure accuracy. In our case, we found that x = 2000. We substitute this value back into the original equation:

0.05(2000) + 0.12(2000 + 5000).

First, calculate each term:
0.05 * 2000 = 100
0.12 * 7000 = 840.

So, 100 + 840 = 940.

Since both sides of the equation are equal, our solution is verified as correct.

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 equation. $$ \left|\frac{2}{3} x-2\right|=\left|\frac{1}{3} x+3\right| $$

Give, in interval notation, the unknown numbers in each description. Three times a number, minus \(5,\) is no more than 7 .

A certificate of deposit for 1 yr pays $25.50 simple interest on a principal of 3400. What is the interest rate being paid on this deposit?

Bonnie earned scores of 90 and 82 on her first two tests in English literature. What score must she make on her third test to keep an average of 84 or greater?

Find the open interval in which \(x\) must lie in order for the given condition to hold. \(y=4 x-8,\) and the difference of \(y\) and 3 is less than 0.001.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

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.