If 1 is subtracted from seven times a certain number,the result is the same as if 31 is added to three times the number. Find thenumber. ( If we let n represent the number to be found, the sentenceIf 1 is subtracted from seven times a certain number, the result is the sameas if 31 is added to three times the number. can be translated into thefollowing algebraic equation: 7n1 = 3n + 31 Solve this equation 7n1 = 3n +31
7n + 0 = 3n +32 7n =3n + 32 7n = 3n + 32
4n= 0n + 32 4n= 32 4n/4 = 32/4 Divide each side by 4 n = 8 Now we substitute the solutionfor n into the original equation to see if it works. 7n 1 =3n + 31 7(8)1 = 3(8) + 31 56 1 = 24+ 31 55 = 55 We must also see if the solution works in theoriginal problem statement. If 1 is subtracted from seven times a certain number,the result is the same as if 31 is added to three times the number. If 1 is subtracted from seven times a certain number (7X 8), the result is the same as if 31 is added to three times the number (3 X8). If 1 is subtracted from seven times a certain number(56), the result is the same as if 31 is added to three times the number(24). If 1 is subtracted from 56, the result is the same as if31 is added to 24. 561 = 31 + 24 55 = 55 We have just solved a first degree equation. ( The source for the problem statement is: Intermediate AlgebraFor College Students by Jerome E. Kaufman |

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