Solve and check: (x-1)/5 - (x+3)/2 = 1- x/4

Question

Accepted Answer

Hello, today we're going to be solving the given equation and then we're going to check its solution. So what we are given is X plus 2/ minus X minus 4/2 is equal to one minus X over eight. Now, since we want to solve for X, we want to go ahead and set the equation equal to zero. In order to do that, we're going to add X over eight to both sides of the equation. And we're going to subtract one to both sides of the equation. And doing this is gonna allow me to rewrite the equation as X plus 2/3 minus X minus 4/ plus X over eight minus one. And I'm gonna go ahead and write one as 1/1 since we're dealing with fractions. Now, what I want to do is eliminate the denominators. On the left hand side, I can go ahead and multiply everything by the greatest common factor in order to eliminate the denominators. And so now we need to think what is the greatest common multiple between 3-8 and one. While all three of these numbers share the greatest multiple of 24 C3 can be multiplied eight times to give you 24, you can multiply two by 12 to give you 24, 8 can be multiplied three times to give you 24 and one times 24 is going to give you 24. So what we're going to do is multiply everything in the equation by 24. So the first term is gonna be multiplied by 24/1. The second term is being multiplied by 24/1. The third term is being multiplied by 24/1. And the last term is being multiplied by 24/1. And on the right hand side, we're also going to multiply zero by 24/1, but anything multiplied by zero is just going to give you zero. Now let's go ahead and simplify the left hand side by using cross cross simplification. 24/3 can be reduced to eight 24/2 can be reduced to 24/8 can be reduced to three and 1/1 times 24/1 is just going to give us 24/1. So we can go ahead and rewrite the equation as eight times X plus two minus 12 times X minus four plus three times X minus 24/1, which can be written as 24 that is going to equal to zero. Now, what I want to do is get rid of the parentheses. And in order to do that, I'm going to distribute eight into X plus two and negative 12 into X minus four. And that's going to give me eight X plus 16 minus 12 X plus 48 plus three, X minus 24 is equal to zero. Now, in order to simplify this, I'm gonna go ahead and combine like terms I can combine eight X negative 12 X and three X together. And that's going to give me negative X, Then I can combine 1648 and - together. And that's going to give me positive 40 And that is going equal to zero. And since we want to solve for X, we can go ahead and just add X to both sides of the equation. And that's going to give us X is equal to 40. So this is the solution that we came up with for the given equation. But now we need to check to make sure that the solution works with the original equation. In order to check that we're gonna go ahead and take the solution of X and plug it into the original equation. And doing this is going to give us 40 plus 2/3 minus -4/2 is equal to 1 -40/8. Now, on the left hand side, 40-plus 2 is going to give us 42 and 40 -4 is going to give us 42 divided by three is going to simplify to give us and 36 divided by two is going to simplify to give us 18. And on the right hand side, 40 divided by eight is going to give us five. So the right hand side is 1 -5. Now, all we need to do is just go ahead and add the numbers on the left hand side and right hand side together and 14 minus 18 is going to give us negative four and one minus five is going to give us negative four. What we are left with is negative for is equal to -4, which is a true statement. And that verifies that X is equal to 40 is going to be our solution. And with that being said, the answer to this problem is going to be be. 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.

Solve and check: (x-1)/5 - (x+3)/2 = 1- x/4

Key Concepts

Rational Expressions

Solving Linear Equations

Checking Solutions

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