How do you solve $- 24 \leq 2 x - 10 < - 6$ $-24\leq 2x - 10< - 6$ ?

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Answer 1 · 2017-05-01T07:29:32

$- 7 \leq x < 2$ $-7≤x<2$

I usually split the inequality into two. So it becomes

$- 24 \leq 2 x - 10$ $−24≤2x−10$

and

$2 x - 10 < - 6$ $2x−10<−6$

Then I'll just solve it.

$- 24 \leq 2 x - 10$ $−24≤2x−10$

$= - 12 \leq x - 5$ $=-12≤x-5$

$= - 7 \leq x$ $=color(red)(-7≤)x$

And

$2 x - 10 < - 6$ $2x−10<−6$

$= x - 5 < - 3$ $=x-5<-3$

$= x < 2$ $=xcolor(green)(<2)$

So combine these two equations to get $- 7 \leq x < 2$ $color(red)(-7≤)xcolor(green)(<2)$

How do you solve −24≤2x−10<−6-24\leq 2x - 10< - 6?