Exercises 27–40 contain linear equations with constants in denomi...

Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation.

x/5 - 1/2 = x/6

Accepted Answer

Hi there. This problem says the solve the given linear equation A over seven minus whatever four equals a over eight. Suddenly rewrite it first, We have a over 7 -1/4 equals a over eight. Now to solve this, we have to have everything with the same denominator, otherwise we don't really add or subtract any of our fractions. So let's try and get a common denominator between all of these fractions first. So we want to find all the multiples of each of the nominators. Let's start with seven. So seven we have 7, 14, 21, 28 and so on. I'll say 63 70. Similarly for the four, we have 48, 12, 16 and so on. So I'll get a few 56 and finally we have our eights, so eight we have 8 16, 24 32 48, 64, 72 and so on, assuming to find which of these numbers is common between all three of our fractions. Let's take a look look here, You have a 28 and the seventh and the 28 and the four, but not in the eight. So you can teach 28, let's keep going if you look here, See we have a 56 here, we also have a 56 here and finally we have a 56 there, So our least common denominator is 56. Now we're gonna use this 56 to get a common denominator between everything. So I'm gonna multiply everything in our fractions by 56. So if I go and rewrite this again, Number seven, that's what I was before. 8/8. Multiplying everything By 56 on both sides. Here We get 56 a over seven -56/ Equals 56 A Over eight. Now we can go ahead and simplify a fraction. So going right out again 56/7 we know that is eight. So we have an eight A. Here we have 56/4 which turns out to be 14. Okay we have 56/8. Well that turns out to be seven within a. Now we have a problem with themselves to solve this. We want to combine our like terms. So unless we have And a. and 14 over here and on the other side let's put on one side I'm gonna subtract a pay, I do that. The -14 stays up there. The eight days cancel each other And I get the the 14 that comes down Now we have seven a -8. A 7 -8 is negative one. So we have negative a. Finally We can divide both sides by -1. I do that. I get 14 equals eight or eight equals 14. So our answer is a girl's 14 which means the answer to our problem is the answer is C okay I hope to help you solve the problem. Thank you for watching. Goodbye

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