/*! 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 69 If a number is added to 4 less t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 69

If a number is added to 4 less than 5 times itself, the result is \(27 .\) Find the number.

Short Answer

Expert verified
The number is approximately 5.1667.

Step by step solution

01

Define the variable

Let the number be denoted by the variable \(x\).
02

Translate the words into an equation

According to the problem, if the number \(x\) is added to 4 less than 5 times itself, the result is 27. This can be written as: \[ x + (5x - 4) = 27 \]
03

Simplify the equation

Combine the like terms in the equation: \[ x + 5x - 4 = 27 \] \[ 6x - 4 = 27 \]
04

Solve for the variable

Add 4 to both sides of the equation to isolate the term with the variable: \[ 6x - 4 + 4 = 27 + 4 \] \[ 6x = 31 \] Then, divide by 6 on both sides to solve for \(x\): \[ x = \frac{31}{6} \] This simplifies to: \[ x = 5.1667 \text{ (approximately)} \]

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.

variable definition
When solving linear equations, the first important step is defining the variable. In our problem, we need to find a number. By assigning a letter, usually 'x', to represent this unknown number, we can convert the problem into a more manageable form. This variable acts as a placeholder for the unknown value we are trying to determine. Once we define 'x', we can use it to set up equations and manipulate them to find the solution.
translating word problems into equations
The next step involves translating the word problem into an algebraic equation. This might seem tricky at first, but with practice, it becomes easier. Consider the problem statement: 'If a number is added to 4 less than 5 times itself, the result is 27.' First, we recognize that the 'number' is 'x'. Then, '4 less than 5 times itself' translates to '5x - 4'. The 'number added to this expression' means we add 'x' to '5x - 4'. Finally, setting this equal to 27, we get the equation: <\br> <\[ x + (5x - 4) = 27 \]>.
combining like terms
Once we have an equation, the next step is to simplify it by combining like terms. Like terms are terms with the same variable raised to the same power. In this equation, 'x' and '5x' are like terms. By adding them together, we simplify the equation: <\br> <\[ x + 5x - 4 = 27 \]>. <\br> This further simplifies to: <\[ 6x - 4 = 27 \]>. Combining like terms makes the equation simpler and easier to solve.
isolating the variable
The last step is isolating the variable on one side of the equation to solve for it. We start with: <\br> <\[ 6x - 4 = 27 \]>. <\br> First, we add 4 to both sides to get: <\[ 6x = 31 \]>. Then, we divide both sides by 6 to isolate 'x': <\[ x = \frac{31}{6} \]>. <\br> This gives us the solution, which is approximately <\[ x = 5.1667 \]>. This process is crucial in solving linear equations as it helps us find the exact 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 the given inequality. Round off your answers to the nearest hundredth where necessary. $$-15.45 \leq 53.67-0.45 t<36.93$$

Perform the indicated operations and simplify as completely as possible. $$x^{2}\left(x^{3}-4 x\right)-\left(2 x^{5}-4 x^{3}\right)$$

Set up an inequality and solve it. Be sure to clearly label what the variable represents. An organization wants to sell tickets to a concert. It plans on selling 300 reserved-seat tickets and 150 tickets at the door. The price of a reserved- seat ticket is to be \(\$ 2\) more than a ticket at the door. If the organization wants to collect at least \(\$ 3,750\), what is the minimum price it can charge for a reserved-seat ticket?

Perform the indicated operations on the given inequality. Sketch the resulting inequality on a number line. \(-4 \leq 4 y \leq 12 ; \quad\) divide each member by 4

An electrician charges \(\$ 45\) per hour for her time and \(\$ 24\) per hour for her assistant's time. On a certain job the assistant worked alone for 4 hours preparing the site, and then the electrician and her assistant completed the job together. If the total labor bill for the job was \(\$ 464,\) how many hours did the electrician work?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

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.