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 the
number. ( If we let n represent the number to be found, the sentence
“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.” can be translated into the
following algebraic equation: 7n – 1 = 3n + 31 Solve this equation 7n – 1 = 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 solution for 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 the
original 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 (7
X 8), the result is the same as if 31 is added to three times the number (3 X
8). 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 if
31 is added to 24. 56 – 1 = 31 + 24 55 = 55 We have just solved a first degree equation. ( The source for the problem statement is: “Intermediate Algebra For College Students” by Jerome E. Kaufman |

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