Question 514918: Hello,
I would like to receive help on this problem
Solve the linear equation ((12+x)/(-4))-5=((5x-7)/(3))+2x+3
please help as soon as possible I had tried multiplying the sides by 4 and 3 but my teacher said what you do to one side you must do to the other as well. so please help thank you in advance.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Your teacher is correct. You cannot multiply one side of the equation by 4 without multiplying the other side by 4 also. And you cannot multiply one side by 3 without multiplying the other side by 3 too.
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You are given the following problem to solve:
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Let's begin by multiplying both sides of this problem by 4. Remember that every term must be multiplied by 4. There are 2 terms on the left side and 3 terms on the right side. All of them get multiplied by 4 as shown below:
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For the first term on the left side (the fraction) we can divide the denominator of -4 into the 4 in the numerator to get -1. This just makes the fraction have a minus sign. We also multiply the 4 times 5 to get 20. On the right side we leave the fraction alone for the time being. But we multiply out the 4 times 2x to get 8x and the 4 times 3 to get 12 and make the whole equation become:
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Next, to eliminate the denominator 3 on the right side, let's multiply all terms of this equation by 3 as follows:
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In the first term on the right side we can cancel the 3 in the denominator with the 3 in the numerator and the equation then becomes:
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Let's do the distributed multiplications for the first term on the left side [3*(-12 - x)] and for the first term on the right side [4*(5x -7)]:
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Next, on the left side multiply the 3*20 to get 60 and on the right side multiply the 3*8x to get 24x and the 3 times 12 to get 36. The equation then is:
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Now remove all the parentheses:
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Then we will begin to solve this equation by collecting all the terms containing x on the left side of the equation and all the numbers on the right side. But first let's add together the 20x and the 24x on the right side to get 44x as shown below:
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Then subtract 44x from both sides. This makes the 3x on the left side become -47x and on the right side the 44x minus the 44x we are subtracting results in zero and the 44x term is therefore gone:
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On the left side, let's combine the -36 and the -60 to get -96. And on the right side let's combine the -28 and +36 to get +8. As a result the equation is now:
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To get rid of the -96 on the right side, let's add +96 to both sides. On the left side this addition causes the -96 to become zero (or to go away). And on the right side the addition of 96 to 8 becomes 104 as shown below:
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Finally, to solve for x, divide both sides by -47 and you get:
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And doing this division on a calculator you get:
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This above process could have been shortened using the following method. Instead of first multiplying both sides by 4 and then multiplying both sides by 3, we could have saved some work by multiplying all terms on both sides by 12 (the common denominator for 4 and 3). In one step that would have made it possible to get rid of the two denominators, but it might have been a little confusing to you. The two separate multiplications, first by 4 and then by 3, might be a little easier to understand, but it does involve a little more work.
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Check all the above work to ensure that I didn't make some dumb mistake in multiplication, division, addition or subtraction. I don't think I did, but once in a while I do so, so check my work. Thanks ...
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I hope this helps you to understand this problem a little bit better and especially makes you aware of whatever you do to one side of an equation, you must also do to the other side to maintain the equality of both sides.
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