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Question 129869: twice the difference of a number and 3 is equal to three times the sum of the number and 5
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let x represent the unknown number.
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The difference of a number and 3 is x - 3
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The sum of the number and 5 is x + 5
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Twice the difference of a number and 3 is therefore 2(x - 3)
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Three times the sum of the number and 5 is therefore 3(x + 5)
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These last two terms are equal. In equation form this is:
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2(x - 3) = 3(x + 5)
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Perform the distributed multiplications on both sides. On the left side multiply the 2 times
each of the terms in the set of parentheses. On the right side multiply the 3 times each
of the terms in its set of parentheses. After these two multiplications the equation is:
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2x - 6 = 3x + 15
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Get rid of the 3x on the right side by subtracting 3x from both sides and you have:
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-x - 6 = 15
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Get rid of the -6 on the left side by adding 6 to both sides to get:
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-x = 21
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You are trying to solve for +x. To change the left side of this equation to +x multiply
both sides by -1 and you change the equation to:
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x = -21
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Hope this helps you to understand the problem.
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