In Exercises 1–14, simplify the expression or solve the equation,...

Question

In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate.

3x/4 - x/3 + 1 = 4x/5 - 3/20

Accepted Answer

Hello, today we're gonna be solving the equation for why? So what we are given is seven Y over six minus Y over three plus two is equal to 11 Y over 12 minus 5/30. Now, for simplicity, we're gonna go ahead and represent two as a rational number and we're gonna do that by placing it over one. So what we currently have is a rational equation. And in order to approach a rational equation, we must eliminate the denominators by looking for a least common multiple between the denominators. So there's five numbers in total in the denominators, we have 631 and 30. And so the question is what is going to be the least common multiple between these five numbers? Well, in this case here, the least common multiple is going to be 60. So what we're going to do is we're going to multiply each term in the equation by in order to solve for Y. So that is going to give us seven Y over six, multiplied by 60/1 minus Y over three, multiplied by 60/1 plus 2/1 multiplied by 60/ and that is going to equal to 11 y over 12, multiplied by 60/1 minus 5/30 multiplied by 60/1. And so now what we're going to do is we're gonna go ahead and eliminate the numerator and denominators in the first term. Six and 60 are both multiples of six. So we can reduce the denominator to one and reduce 60 to in the second term. We have three in the denominator and 60 in the numerator. Both are multiples of three. So we can reduce the denominator to one and 60 to 20. In the third term, there's nothing further we can do. So we're just going to multiply two and 60 together. In the fourth term, we have 12 in the denominator and 60 in the numerator, which are both multiples of 12. And that is going to reduce the denominator to one and the numerator to five. And for the last term, we have 30 in the denominator and 60 in the numerator, which are both multiples of 30. So that's gonna reduce the denominator to one and reduce 60 to 2. So what we are left with is 10 times seven Y minus Y times 20 plus two times is equal to 11 Y times five minus five times two. And so what we're going to do is we're going to multiply the terms together times seven, Y is going to give us 70 Y negative Y times 20 is going to give us negative 20 Y and two times 60 is going to give us 100 and 20 that is going to equal to five times 11 Y which is 55 Y minus five times two, which is going to give us 10. On the left hand side, we can go ahead and combine the light terms of 70 Y and negative 20 Y and that is going to give us 50 Y plus 100 and 20 is equal to 55 Y minus 10. Now, what we're going to do is we're going to solve for Y by moving all the Y terms to the left hand side and moving all the constants to the right hand side. So we're going to subtract 55 Y to both sides of the equation and we're going to subtract 100 and 20 to both sides of the equation that is going to leave us with negative five, Y is equal to negative 130. And finally, in order to solve for Y, we're going to subtract or divide both sides by negative five and that is going to give us Y is equal to positive 26 which is going to be the solution to this given equation. And with that being said, the answer to this problem is going to be C so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate. 3x/4 - x/3 + 1 = 4x/5 - 3/20

Key Concepts

Combining Like Terms

Finding a Common Denominator

Isolating the Variable

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