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\n" ); document.write( "***
\n" ); document.write( "Since the integers are consecutive, the second will be exactly one greater than the first. Thus, you can call the first (the lesser) integer x, and the second (larger) one x + 1.
\n" ); document.write( "***
\n" ); document.write( "Let us model the statement \"when the lesser . . . is added to 5 times the larger number, the result is 71\" with an equation. Let us figure each part out piece by piece:
\n" ); document.write( "\"the lesser of two consecutive integers\": x
\n" ); document.write( "\"the larger number\": x + 1
\n" ); document.write( "\"5 times the larger number\": 5(x + 1)
\n" ); document.write( "\"when the lesser of two consecutive integers is added to 5 times the larger number\": x + 5(x + 1)
\n" ); document.write( "\"when the lesser of two consecutive integers is added to 5 times the larger number, the result is 71\": x + 5(x + 1) = 71
\n" ); document.write( "Therefore, our equation to model this statement is x + 5(x + 1) = 71
\n" ); document.write( "***
\n" ); document.write( "Now we simply solve the equation.
\n" ); document.write( "x + 5(x + 1) = 71
\n" ); document.write( "Distribute the 5 through the (x + 1): x + 5x + 5 =71
\n" ); document.write( "Add like terms: 6x + 5 = 71
\n" ); document.write( "Subtract 5 from both sides: 6x = 66
\n" ); document.write( "Divide both sides by 6: x = 11
\n" ); document.write( "***
\n" ); document.write( "Thus, x, which represents the value of the lesser integer, is equal to 11. Since the greater integer is x + 1, it is equal to 12.
\n" ); document.write( "***
\n" ); document.write( "Therefore, the integers are 11 and 12.
\n" ); document.write( "Let me know if you need any further clarification! =) \n" ); document.write( "