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