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Solve each equation, if possible.$$\frac{3}{8}(14-u)=-3 u+6$$
$\mathrm{u}=(6 / 21)$
Precalculus
Algebra
Chapter 2
Equations, Inequalities, and Problem Solving
Section 2
More about Solving Equations
Algebra Topics That are Reviewed at the Start of the Semester
Equations and Inequalities
Oregon State University
McMaster University
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Okay, We're gonna solve 3/8 times 14 minus you equals negative. Three. You plus six. And the first thing I want to do is multiply both sides by eight. Because that will allow me to clear out the denominator. So now I have three times 14 minus you equals eight times negative. Three You plus six from the next step will distribute. So three times 14 is 42 three times negative view is negative. Three u eight times negative three. You is negative. 24 u in eight times six is positive. 48. Then I want all the use on one side and my integers on another. So I'm an ad 24 u and at the same time, I'm going to subtract 42. So I get 21 u equals six. Since my goal is to get to you alone, all divide by 21 toe, undo that multiplication, and then I'll simplify my answer, and I get 2/7. So let's check that this actually works. I'm gonna plug into this addition where the eights have already been cleared out of the denominator and it'll still work. So let's do that. I have three times 14 minus 2/7 equals eight times negative three times to seventh plus six. And I want to see if that is indeed correct. So let's go ahead and start distributing Here. I have three times 14 which is 42 three times negative to seventh is negative. 6/7 equals eight times negative, 6/7 plus six. So now what I will do is distribute on the right. So 42 minus 6/7. I'm still checking. Is this true? And eight times 967 is negative. 48 7th and eight times six is 48. I'm not really thrilled with my fractions. So I will continue the concept of busting out those fractions by Let's just multiply by seven here. And so now I am looking at 42 times seven, which is 294. The seven here is gonna cross off so minus six, is that equal to seven? Here again? Well, cross off. So I'll have negative 48 and then 48 times seven is 336. Okay, so let's just clean this up a bit. 294 minus six is 288 and 336 minus 48 is also 288. So you equals two fists
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