An algebra problem by Rahil Sehgal

Algebra Level 4

$\large |2^{x+1} -1| + |2^{x+1} +1| = 2^{|x+1|}$

Find the integer value of $x$ satisfying the above equation.

Notation: $|\cdot|$ denotes the absolute value function .

1 solution

Guilherme Niedu
May 2, 2017

If $x \geq - 1$ :

$\large \displaystyle 2^{x+1}-1 + 2^{x+1}+1 = 2^{x+1}$

$\large \displaystyle 2^{x+2} = 2^{x+1}$

$\large \displaystyle x+2 = x+1$

Which has no solution. If $x<-1$ :

$\large \displaystyle 1- 2^{x+1} + 2^{x+1}+1 = 2^{-x-1}$

$\large \displaystyle 2 = 2^{-x-1}$

$\large \displaystyle 1 = -x-1$

$\color{#3D99F6} \boxed{\large \displaystyle x=-2}$

Thank you sir.(+1)

Rahil Sehgal - 4 years, 1 month ago

You're welcome :)

Guilherme Niedu - 4 years, 1 month ago