Problem

Solve each equation, if possible. $$ 0.05 a+0.01(…

02:34

Problem 58 Hard Difficulty

Solve each equation, if possible.
$$
\frac{3}{8}(14-u)=-3 u+6
$$

Answer

$\mathrm{u}=(6 / 21)$

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Precalculus

Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 2

More about Solving Equations

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Video Transcript

Okay, so I want to solve 3/8 times 14 minus you equals negative. Three. You plus six. I'm gonna start by clearing out that denominator. And I'll do that by multiplying both sides by eight. And what That doesn't The left is crosses that off and leaves me with 13 times 14 strike three times 14 minus you. And on the right, I'll have the eight times the negative three. You plus six. Now I want to distribute. So three times 14 is 42 three times negative view is negative. Three u and on the right, eight times negative. Three. You is negative. 24 u in eight times six is positive. 48. So I want to get, like, terms on the same side. I'll go ahead and get my use on the left by adding 24 u, which gives me 42 plus 21. You equals 48 and then I'll want to subtract 42. Since my goal is to get that 1st 21 you alone and then you alone from there. So to do that, I will divide by 21 to undo that multiplication and simplify you get u equals 2/7. All right, so we want to check that two sevens works, and you could plug it into the very original one. Or you could plug it into this version. It's a little bit easier to plug into this version here, so I'm gonna do that one. And what that means is, every time I see you, I will replace it with 2/7. So three times 14 minus 2/7 equals eight times negative. Three times to seventh plus six. That's what we want to check. So I'm gonna go ahead and just start to write this out by distributing and I'm not gonna find the ValuJet. I'm just gonna write it. Multiplied outs are set up for multiplying out, and I'll show you what I mean. So three times 14 minus three times 2/7 is that equal to and here we're gonna have to do a little clean up before we can do this. So eight times this thing is negative. 6/7 plus six. Okay, three times 14 is 42. This is negative 6/7 and I want to know is that equal to? And now we'll actually start to distribute eight times negative 6/7 is negative. 48 7th and eight times six is 48. So first let's go ahead and subtract. 42 is negative. 6/7 equal to negative, 48 7th plus six. Now, I'm not loving the fractions, so let's go ahead and clear them out. And I'm gonna do the same strategy I did before. Multiply everything by seven and you end up with negative six equals negative. 48 plus 42 in great news, Negative six does equal this, so we know that 2/7 is correct.

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