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How do you solve $2 n + 12 = 5 n$ $2n+12=5n$ ?

1 Answer

Nov 19, 2015

Following basic rules for manipulating equations, you get
$n = 4$ $n=4$

Explanation:

Given any equation, here are some things you can do to both sides that will keep the equation valid:

add or subtract the same amount to/from both sides
multiply both sides by the same amount
divide both sides by the same amount if the amount is not $0$ $0$
exchange the two sides

Given the above rules:
We can subtract $2 n$ $2n$ from both sides of $2 n + 12 = 5 n$ $2n+12=5n$
to get
$XXX 12 = 3 n$ $color(white)("XXX")12=3n$

We can exchange the sides of $12 = 3 n$ $12=3n$
to get
$XXX 3 n = 12$ $color(white)("XXX")3n=12$

We can divide both sides of $3 n = 12$ $3n=12$ by $3$ $3$
to get
$XXX n = 4$ $color(white)("XXX")n=4$

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