How do you solve $abs(x/7)=3$ ?

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Answer 1 · 2017-06-12T03:43:36

$x=+-21$

Solve:

$abs(x/7)=3$

$absa=+-a$ There are two equations to solve: one is positive, the other is negative.

Positive equation.

$x/7=3$

Multiply both sides by $7$ .

$color(red)cancel(color(black)(7))xx x/color(red)cancel(color(black)(7))=3xx7$

$x=21$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Negative equation.

$-x/7=3$

Multiply both sides by $7$ .

$-x=3xx7$

$-x=21$

Divide both sides by $-1$ .

$(color(red)cancel(color(black)(-))x)/(color(red)cancel(color(black)(-))1)=21/(-1)$

$x=-21$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solution:

$x=+-21$

How do you solve abs(x/7)=3abs(x/7)=3?