document.write( "Question 159625: The second of three numbers is 7 less than 3 times the first. The third is 13 less than 6 times the first. If twice the first is decreased by the third, the result is -3. Find the three numbers. \n" ); document.write( "
Algebra.Com's Answer #117757 by ankor@dixie-net.com(22740)\"\" \"About 
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The second of three numbers is 7 less than 3 times the first. The third is 13 less than 6 times the first. If twice the first is decreased by the third, the result is -3. Find the three numbers.
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\n" ); document.write( "Let x = \"the first number\"
\n" ); document.write( "Let y = \"the second number\"
\n" ); document.write( "Let z = \"the third number\"
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\n" ); document.write( "Write an equation for each statement:
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\n" ); document.write( "'The second of three numbers is 7 less than 3 times the first.\"
\n" ); document.write( "y = 3x - 7
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\n" ); document.write( "\" The third is 13 less than 6 times the first.\"
\n" ); document.write( "z = 6x - 13
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\n" ); document.write( "\"If twice the first is decreased by the third, the result is -3.\"
\n" ); document.write( "2x - z = -3
\n" ); document.write( ":
\n" ); document.write( "Find the three numbers.
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\n" ); document.write( "Note that the 2nd equation is: z = (6x-13), substitute this for z in the last equation:
\n" ); document.write( "2x - (6x-13) = -3
\n" ); document.write( "2x - 6x + 13 = -3; (removing the brackets, changes the sign of 13)
\n" ); document.write( "2x - 6x = -3 - 13
\n" ); document.write( "-4x = -16
\n" ); document.write( "x = \"%28-16%29%2F%28-4%29\"
\n" ); document.write( "x = +4
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\n" ); document.write( "Recall that z = 6x -13, substitute 4 for x
\n" ); document.write( "z = 6(4) - 13
\n" ); document.write( "z = 24 - 13
\n" ); document.write( "z = 11
\n" ); document.write( "and
\n" ); document.write( "y = 3x - 7; substitute 4 for x again
\n" ); document.write( "y = 3(4) - 7
\n" ); document.write( "y = 12 - 7
\n" ); document.write( "y = 5
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\n" ); document.write( ":
\n" ); document.write( "Check our solution in the statement:
\n" ); document.write( "\" If twice the first is decreased by the third, the result is -3.
\n" ); document.write( "2(4) - 11 = -3 \n" ); document.write( "
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