Question

Solve each of the following equations for x.


a) 3x - 8 =29 b) 3 ( x - 8 ) = 28

c) 3 (x - 8) + 17 =29 d) 7x + 12 = 3x - 8

Answer 1

$3x - 8 =29 \\ \\ 3x = 29 + 8 \ / \ add \ 8 \ to \ each \ side \\ \\ 3x = 37 \ / \ simplify \\ \\ x = \frac{37}{3} \ / \ divide \ each \ side \ by \ 3 \\ \\ Answer: \fbox {x = 37/3} \ or \ \fbox {x = 12.3333}$

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$3 ( x - 8 ) = 28 \\ \\ x - 8 = \frac{28}{3} \ / \ divide\ each \ side \ by \ 3 \\ \\ x = \frac{28}{3} + 8 \ / \ add \ 8 \ to \ each \ side \\ \\ x = \frac{52}{3} \ / \ simplify \\ \\ Answer: \fbox {x = 52/3} \ or \ \fbox {x = 17.3333}$

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$3 (x - 8) + 17 =29 \\ \\ 3(x - 8) = 29 - 17 \ / \ subtract \ 17\ from \ each \ side \\ \\ 3(x - 8) = 12\ / \ simplify \\ \\ x - 8 = \frac{12}{3} \ / \ divide \ each \ side \ by \ 3 \\ \\ x - 8 = 4 \ / \ simplify \\ \\ x = 4 + 8 \ / \ add \ 8 \ to \ each \ side \\ \\ x = 12 \ / \ simplify \\ \\ Answer: \fbox {x = 12}$

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$7x + 12 = 3x - 8 \\ \\ 7x + 12 - 3x = -8 \ / \ subtract \ 3x \ from \ each \ side \\ \\ 4x + 12 = -8 \ / \ simplify \\ \\ 4x = -8 - 12 \ / \ subtract \ 12 \ from \ each \ side \\ \\ 4x = -20 \ / \ simplify \\ \\ x = - \frac{20}{4} \ / \ divide \ each \ side \ by \ 4 \\ \\ x = -5 \ / \ simplify \\ \\ Answer: \fbox {x = -5}$