How do you solve $-1+x=1/3$ ?

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Answer 1 · 2016-07-28T18:37:27

$x=4/3$

$color(red)("Using first principles method")$

Given: $" "color(brown)(-1+x=1/3)$

Add 1 to both sides

$color(brown)(-1color(blue)(+1)+x=1/3color(blue)(+1))$

But $-1+1=0" and "1/3+1=1/3+3/3=4/3$

$=0+x=4/3$

$x=4/3$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(red)("Using shortcut method")$

move the $-1$ to the other side of the = and change its sign

$color(brown)(-1+x=1/3)color(blue)(" "->" "x=1/3+1)$

But 1 is the same as $3/3$

$x=1/3+3/3=4/3$

How do you solve -1+x=1/3-1+x=1/3?