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

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Hello. Today I'm going to be solving an equation for X. So the equation given to us is X plus 2/ minus. The quantity X minus 4/2 is equal to one minus X over eight. Now, since we want to sulfur X we need to go ahead and set this equation equal to zero. In order to do that. I'm going to subtract one to both sides of the equation And I'm going to add X over 8 to both sides of the equation. Doing so is going to give me the quantity X plus 2/3 minus the quantity X minus 4/2 minus one plus X over eight equal to zero. Now we want to go ahead and combine this whole left hand side into a single quantity. And in order to do that we need to go ahead and identify what the lowest common denominator is between these four values. Well one can be represented as a ratio as 1/ is the same thing as one. So we need to find a common denominator. Between all four of these denominators were given the terms 321 and eight. Now a common multiple between these four numbers is going to be 24. So we need to multiply each of these quantities by a number that's going to give us a denominator with 24. While the first quantity can be multiplied by 8- because three times eight gives us 24. And if we change the denominator we must change the numerator. The second quantity X minus 4/2 can be multiplied by 12/12. 1/1 can be multiplied by 24/ X over eight can be multiplied by 3/3. Now multiplying these quantities together is going to give me eight times the quantity X plus 2/ minus 12 times the quantity X minus 4/24 minus 20 for over 24 plus three X over 24 is equal to zero. Now that every quantity here is over the same denominator, I can combine everything together or I can go ahead and multiply the entire equation by 24 to eliminate the denominators And so multiplying the entire equation by 24 means we're going to distribute 24 to every term in this equation. Doing so is going to cancel out each of the denominators leaving us with eight times the quantity X plus two minus 12 times the quantity X minus four minus 24 plus three X equal to zero. And now we need to simplify the left hand side. In order to open up these parentheses, I'm gonna distribute eight and 12 into its respective quantities. So I'm gonna distribute 82 X plus two and I'm distributing negative 12 X minus four. Doing so is going to give me eight X plus minus 12 X plus 48 minus 24 plus three X is equal to zero. Now I'm going to continue adding the like terms together eight X. And negative 12 X. And three X. Can be combined together to give me negative X. And 1648 and -24 can be combined together to give me positive 40 and this is going to equal to zero. Now in order to Sulfur X, I can just go ahead and add X to both sides of this equation. And what I'm left with is X is equal to 40. So this is the value of X that we have solved for. But now we need to check to make sure that this value of 40 works with our original equation. Well in order to do that, what I can go ahead and do is take this value of X and directly plug it in for every X in our original equation. So doing so is going to give me 40 plus 2/3 minus 40 minus 4/2 is equal to one minus 40/8. And now 40 plus two is going to give me 40 to 40 minus four is going to give me 40/8 reduces to five. And so simplifying this, 42/3 is going to leave me with 14 36/2 is gonna leave me with negative 18 And this is equal to 1 -5. Now 14 -18 is going to give me - And this is going to equal to 1 -5, which is also negative four. So since both sides of the equation are equal to each other, this value of X is going to be our solution, and that means that the answer to this problem is going to be. Be so. I hope this video helps you in understanding how to solve this equation for X, 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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