You can put this solution on YOUR website! Given:
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7(2x + 6) = 1
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To solve this equation for x, begin with the distributed multiplication on the left side.
Do this multiplication by multiplying 7 times each of the terms inside the parentheses.
The 7 times 2x is 14x and the 7 times +6 is +42. Substituting these two products changes
the equation to:
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14x + 42 = 1
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Next you need to get the term that contains the x on one side of the equation and the numbers
on the other side. Do this by getting rid of the +42 on the left side ... and you do that
by subtracting 42 from both sides. When you take 42 away from the left side you are left
with just 14x and when you take 42 away from the right side you get 1 - 42 = -41. So
the equation that results is:
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14x = -41
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Finally you can solve for x by dividing both sides of the equation by 14. On the left side
the 14x divided by 14 is just x. On the right side the -41 divided by 14 is -41/14 and
it cannot be reduced further because the numerator and denominator do not have common factors.
You could change the right side to -2 13/16, but it doesn't gain you much. So the answer
to this problem is:
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x = -41/14
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You can check this answer by substituting it back into the original problem that you were given
and then do the math to see if both sides of the equation are actually equal. So start with:
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7(2x + 6) = 1
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Substitute -41/14 for x and you get:
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7(2*(-41/14) + 6) = 1
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Multiply the 2 times the -41/14 to get -82/14 and this makes the equation become:
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7(-82/14 + 6) = 1
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But because the denominator and numerator of -82/14 are both even numbers, they can both
be divided by 2 without changing the basic value of the fraction. -82/14 is equal to
-41/7. Substitute this and you have:
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7(-41/7 + 6) = 1
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Now multiply both terms in the parentheses by 7. When you multiply 7 times -41/7 the multiplication
cancels out the denominator and you are left with just -41. And when you multiply
7 times 6 you get + 42. So the equation becomes:
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-41 + 42 = 1
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and the two terms on the left side combine to give +1. So the equation therefore is:
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1 = 1
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and since both sides are obviously equal, the value that we found for x works. Therefore,
we can say that x = -41/14 is the correct solution to this problem.
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Hope this discussion helps you to see the process for solving equations of this type.
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