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# How do you solve $7n - 5 = 5n + 7$?

Last updated date: 19th Jul 2024
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Hint: In the given problem we need to solve this for ‘n’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘n’ terms one side and constants on the other side of the equation.

Complete step-by-step solution:
Given, $7n - 5 = 5n + 7$.
We transpose ‘5n’ which is present in the right hand side of the equation to the left hand side of the equation by subtracting ‘5n’ on the left hand side of the equation.
$7n - 5n - 5 = 7$
$2n - 5 = 7$
We transpose negative 5 to the right hand side of the equation by adding 5 on the right hand side of the equation.
$2n = 7 + 5$.
$2n = 12$
Divide the whole equation by 2,
$n = \dfrac{{12}}{2}$
$\Rightarrow n = 6$
$7(6) - 5 = 5(6) + 7$
$42 - 5 = 30 + 7$
$\Rightarrow 37 = 37$