💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Watch this step-by-step video, matched to your homework problem.

Try Numerade Free for 30 Days

Like

Report

In $3-20,$ solve each equation and check.$$\frac{a-1}{4}=\frac{8}{a+3}$$

$\{-7,5\}$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 7

Solving Rational Equations

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Oregon State University

Harvey Mudd College

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

04:04

In $3-20,$ solve each equa…

04:08

02:26

04:00

06:47

05:33

00:44

Solve each equation.$$…

00:31

Use the Laws of Logarithms…

01:04

00:51

Solve each equation. Check…

All right. Hey, guys. So, in this problem, we have a minus one over four equals eight over eight plus three. Our goal is to solve for a and verify that are solutions air correct. So let's start. We're gonna start by getting our our eight terms on all out of the denominator. So we're gonna do is we're gonna multiply by a plus three. The quantity of April's to be on both sides on our goal is to get the right hand side without an A A term in the denominator. And that's what we're gonna achieve the April stories. Cancel On the right hand side, We're just left with the value eight on our left hand side. We have a plus three times the quantity a minus one over four. Just so we make this problem a little bit easier for ourselves. What I'm gonna do, I'm gonna cancel out the four from the denominator on the left side as well. Basically wants by four on both sides getting rid of the dot the denominator on the left hand side as well. So the forest cancel out. We're left with a plus. Three times a minus one equals 32. And let's simplify this by simplifying mean expand the left hand side. We're gonna get a square minus a plus three a minus three that's going to equal 32. Let's simplify this part. We have a square plus two. A minus three equals 32 and subtract 32 from both sides. We get a squared plus two a minus 35 minus 35 this up and minus 35 is equal to zero. So let's bring this up all the way here, so it's easier to solve. We have more room a square close to a minus 35. Factoring that we're going to get a plus seven times a minus five, that's gonna equal zero. So we know that a plus seven equals zero or a minus five is equal to zero. So our solution said, is gonna be a equals five comma minus seven. And let's verify this on the second page. So the equation that we're trying to verify is a minus. One over four equals eight over a plus three value. The first value. Let's try to verify a equals 25 because our two values are five and five and negative seven. So our first value will verify is deposited five. So left hand side. If we plug in a we're gonna have five minus one over four five minus one is for for over four is equal to one. And on our right hand side, we're gonna have eight over five plus 35 stories. Eights of the denominator is now eight and eight. Over eight is equal to one. Left hand side, right hand side or equal. So we know that's true. Equals five verified to be correct. Now let's try a equals minus seven. Now on the left hand side, if we plug in a equals minus seven would have minus seven minus one, divided by four. That's going to be equal to minus eight over four, which is going to be equal to mine. This too. Then we have our right hand side. We have each over minus seven plus three minus seven plus three is equal to minus 48 Divided by minus four is equal to minus two. We have our left hand side in the right hands out of the same. So a equals minus seven is also a verified solution. So we can definitively say that a was five and a equals minus seven are our correct values. And so it's just raised the stray marks right here. So this, uh, thing these solutions in the red box are the answers to the equation. A minus one over four equals eight over April's three. Thanks for listening.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, the absolute value or modulus |x| of a real number x is its …

In $3-20,$ solve each equation and check.$$\frac{1}{4} a+8=\frac{1}{…

In $3-20,$ solve each equation and check.$$18-\frac{4}{b}=10$$

In $3-20,$ solve each equation and check.$$\frac{2 x}{3}+1=\frac{3 x…

In $3-20,$ solve each equation and check.$$\frac{3}{a}+\frac{1}{2}=\…

In $3-20,$ solve each equation and check.$$\frac{4}{y+2}=1-\frac{8}{…

In $3-20,$ solve each equation and check.$$\frac{x}{2}=\frac{3}{2 x+…

Solve each equation.$$\frac{8(a-5)}{3}=2(a-4)$$

Use the Laws of Logarithms to evaluate the expression.$$\log _{6} 9+\log…

Solve each equation.$$8 a-2(3 a-1)=6$$

Solve each equation. Check each result. See Example 3.$$-\frac{5}{8}…

01:02

Solve each proportion for the variable.$\frac{x-1}{15}=\frac{2}{5}$

00:23

List the values of the variables for which the rational expression is undefi…

01:09

Write each rational expression in simplest form and list the values of the v…

In $13-24,$ divide and express each quotient in simplest form. In each case,…

01:49

In $25-30,$ perform the indicated operations and write the result in simples…

02:39

In $18-23,$ write and solve an equation or an inequality to solve the proble…

03:32

In $3-20,$ solve each equation and check.$$\frac{7}{2 x-3}=\frac{4}{…

00:19

In $3-7,$ write the reciprocal (multiplicative inverse) of each given number…

02:50

01:58

In $15-26,$ find and graph the solution set of each inequality.$$\le…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.