I have this statement:
If $a$ belongs to the interval $[- 4, - 1]$ and $b$ belongs to the interval $[- 2, 3]$, what interval does it contain? all possible values of $(2a - b)$?
I have developed it, but according to the guide my answer is incorrect and I would like to know why.
$-4 \leq a \leq -1$, multiply by $2$
$-8 \leq 2a \leq -2$
Now, the interval of $b$ is:
$-2 \leq b \leq 3$
I know the extreme values of each interval, I will subtract the interval of $ b$ :
$-8 - -2 \leq 2a - b\leq -2 -3$
$-6 \leq 2a - b \leq -5$, so my answer is: $[-6,-5]$
I would like to know why, my development is incorrect. Thanks in advance.