Solve and check. 3.47 a=7.1482

Name: Problem 87, Chapter 5: Prealgebra and Introductory Algebra
Uploaded: 2020-06-21T20:43:23-08:00
Duration: 3 min 58 s
Channel: Ethan Somes
Description: Solve and check. 3.47 a=7.1482

Key Concepts

Linear Equations

A linear equation is an algebraic expression where each term is either a constant or the product of a constant and a single variable raised to the first power. Such equations form straight lines when graphed and serve as a foundational element in algebra, requiring methods like addition, subtraction, multiplication, or division to solve for the variable.

Isolating the Variable

The process of isolating the variable involves manipulating the equation to keep the unknown on one side while moving all other terms to the opposite side. This typically includes dividing or multiplying both sides of the equation by the same number, a fundamental step necessary for solving linear equations.

Inverse Operations

Inverse operations are maneuvers used in algebra that reverse the effect of an operation, such as using division to counteract multiplication. This concept is vital in solving equations since it allows one to systematically eliminate coefficients attached to the variable, thereby simplifying the equation and isolating the desired unknown.

Solution Verification

Solution verification involves substituting the obtained value back into the original equation to confirm that it satisfies the equation. This step ensures that no mistakes were made during the manipulation process and that the solution genuinely resolves the equation as intended.

Transcript

00:01 So here we are solving the equation 3 .47a equals 7 .1482.

00:11 So we want to solve for a.

00:13 So here we have to divide by 3 .47 on both sides.

00:18 Currently, a is being multiplied by 3 .47, and so we want to undo that by dividing.

00:24 So here we have these cancel, and we end up with just a on the left.

00:28 And whatever this quotient is on the right.

00:31 So let's do this quotient out.

00:32 So i could divide 7 .1482 divided by 3 .47, and actually i'm going to multiply both of these by 10 in order to make the long division easier.

00:44 So what that really is doing is, i'll use a different color here, multiplying by 10 over 10, which is the same as 1.

00:53 So i'm not changing the value.

00:55 If i made me feel better, i can multiply the other side by 1 as well.

00:59 Again, we still are equal here.

01:01 So what that does is it gives me the numbers 714 .82 divided by, oh, i'm actually one to multiply by 100, excuse me.

01:13 714 .82 divided by 347.

01:17 That is going to give me an easier time working with these numbers doing long division.

01:21 So here we have 714 .82 .347.

01:27 You can also do this on your calculator if you want.

01:29 I'm doing it out so you can see my thinking.

01:32 Okay, so here we have how many times this 347 going to 7, none, 171, none, 714.

01:40 I'm going to say it goes in twice because i know 300 times 2 is 600 and 300 times 3 is 900, so it's only going to go in twice.

01:50 I'm going to use this area over here for a little bit of scratch work.

01:53 So 347 times 2.

01:56 It'll be 14, 9, 6, 6994...

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