Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

The sum of two consecutive odd integers is 15 more than the next odd integer. Find the three integers.

$$\{17,19,21\}$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Missouri State University

Oregon State University

McMaster University

Idaho State University

Lectures

01:09

Solve each problem.Fin…

03:45

Write an equation and solv…

01:36

The sum of three consecuti…

01:39

The sum of the squares of …

03:46

Find three consecutive odd…

00:38

00:46

The sum of the first and t…

01:01

Solve each problem involvi…

00:40

Set up an algebraic equati…

01:03

01:15

Find three consecutive eve…

03:33

Translate into an equation…

00:54

All right. So for this question, we have another leader equation that we're not to solve for. And it's linear because the X value that we're gonna be looking for is in the powers of one. And again, we're gonna be using the fact that addition and subtraction well into each other and multiplication and the mission more under each other. So this problem we have three consecutive odd integers. But we also know that the sum of two consecutive odd integers is 15 more than the next odd integer. We have to find all three of these integers. So basically with three consecutive odd integers and it's important to note that the authenticators are separated by us by one integer. So it goes from let's take, for example, 3 to 5 to seven. They're going to skip one one integer, which is gonna be an even number. So in this case, um, were given that the third and teacher yes, equal to the sum of two consecutive integers minus 15. So let me repeat it again. So we know that the sum of two consecutive integers is 15 more than the mics. Odd integer. So we know that each waken say, for example, the first to audit teachers. They're gonna be just x And then, of course, the next audit teacher is gonna be explicit too. And then our third odd integer is gonna be X plus four. So now we were took part This in an equation going that the some off the first two. So that's X plus X plus two X plus. Yeah, that's killed is 15 greater than the next odd and teacher. So this value is greater then the third advantage er by a number 15. So we can look at this in two different ways. In order for it to equal the third odd integer, we would have to subtract this value with minus 15 because it's 15 greater than that they're not in teacher now. A third odd integer is X plus four again, this is our third out into jury here. Excuse for I'll keep it in apparent disease us not to confuse. So this is our first advantage. Er our second advantage er and Richard Odd integer these air consecutive authenticators and we know that I were third. Odd temperature is equal to the sum of the first to augment injures minus 15. Yeah, because again, just to reiterate the sum of the two consecutive odd integers is 15 more than the next odd integer. Okay, so now we can simplify, rearrange and isolate To find what X So in this case, or just simply have X plus X plus two minutes 15 for simply collects and its 13 it's equal to experts. For now, we're gonna rearrange the X to the left side of the equation. So we're going to subtract X from both sides of the equation. We have X minus 13 is equal to X minus X zero. So we're not just for we're gonna add 13 people sides of the equation to isolate our X value. Oh, yeah, Work plus 13. So therefore our X value is equal to 17. So remember our first audience pictures just X. Our second one is X Plus two, and our third consecutive audit teacher is X plus four. So we're just gonna plug in 17 to each one. Our first interview is just gonna be 17. Our second one is gonna be something close to which is just thinking. And then our third one is going to be 17 plus four, which is 21. So these are our three consecutive odd integers, and we can quickly check this by observing the fact that 17 plus 19 to the sound here 17 plus 19, um, equal to it's 35 No. 36. So this is gonna able to 36 and we have to take 15 away from this one. Started to get our dirt on in the future, which, indeed that's up to 21.

View More Answers From This Book

Find Another Textbook

01:44

Find the unknown.$$(3 z-4)^{2}=64$$

01:29

Find the unknown.$$6 y^{2}+9=4 y^{2}-45$$

02:14

Find the unknown.$$(x+1)(2 x-3)=12$$

01:14

Complete the square in each of the following by putting in the form $(x+B)^{…

02:19

Determine if the given set is a function.$h=\{(3,-5),(4,-5),(7,11),(11,1…

02:41

Solve each of the quadratics by first completing the square. When the roots …

01:30

Determine if the given set is a function.$V=\{(4,2),(5,3),(4,7),(9,-22)\…

03:29

The length of a rectangle is two feet less than three times its width. If th…

03:30

In each of the following exercises, solve the given inequality.$$\frac{1…

05:03

Today, Maria's age is 5 years less than twice Louie's age. In five…