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

Oct 10, 2017

$x = 5 \text{ or } - 4$

Explanation:

Rearranging equation, $\left\mid - 2 x + 1 \right\mid = 9$

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

For the $\textcolor{b l u e}{\text{negative}}$ case:
$\left\mid - 2 x + 1 \right\mid = - \left(- 2 x + 1\right) = 9$

$\implies + 2 x - 1 = 9$

$\implies + 2 x = 9 + 1 = 10$

$\implies x = \frac{10}{2} = 5$

For the $\textcolor{red}{\text{positive}}$ case:
$\left\mid - 2 x + 1 \right\mid = \left(- 2 x + 1\right) = 9$

$\implies - 2 x = 9 - 1 = 8$

$\implies x = \frac{8}{-} 2 = - 4$

So, $x = 5 \text{ or } - 4$