How do you solve the equation $| 1 - 2 x | = 9$ $abs(1-2x)=9$ ?

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Answer 1 · 2017-10-10T10:24:13

$x = 5 or - 4$ $x=5 " or "-4$

Rearranging equation, $| - 2 x + 1 | = 9$ $abs(-2x+1)=9$

We know that either $- 2 x + 1 = 9$ $−2x+1=9$ or $- 2 x + 1 = - 9$ $−2x+1=−9$

For the $negative$ $color(blue)("negative")$ case:
$| - 2 x + 1 | = - (- 2 x + 1) = 9$ $abs(-2x+1)=-(-2x+1)=9$

$\Rightarrow + 2 x - 1 = 9$ $=>+2x-1=9$

$\Rightarrow + 2 x = 9 + 1 = 10$ $=>+2x=9+1=10$

$\Rightarrow x = \frac{10}{2} = 5$ $=>x=10/2=5$

For the $positive$ $color(red)("positive")$ case:
$| - 2 x + 1 | = (- 2 x + 1) = 9$ $abs(-2x+1)=(-2x+1)=9$

$\Rightarrow - 2 x = 9 - 1 = 8$ $=>-2x=9-1=8$

So, $x = 5 or - 4$ $x=5 " or "-4$