1. ## Absolute Values

Hi

For the question:

Solve for x: abs(x-1) + 3*abs(x+1) ≤ 2

I've tried to obtain the answer using algebra several times but can't seem to. (The answer is x = -1). Could someone please show me how to do this question?

2. You can consider different cases to solve this

$\displaystyle |x-1|+3|x+1|\leq 2$

Case 1: $\displaystyle x\leq -1$

$\displaystyle -(x-1)-3(x+1)\leq 2$
...
$\displaystyle x\geq -1$

Case 2: $\displaystyle -1<x<1$

$\displaystyle -(x-1)+3(x+1)\leq 2$
...
$\displaystyle x\leq -1$

Case 3: $\displaystyle x\geq 1$

$\displaystyle (x-1)+3(x+1)\leq 2$
...
$\displaystyle x\leq 0$

Only case 1 gives solution, i.e. $\displaystyle x=-1$

Hope this helps!