How do you solve the inequality $- 6 < x + 3 < 6$ $-6 < x + 3 <6$ ?

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Answer 1 · 2016-06-03T19:59:35

$- 9 <$ $-9<$ $x < 3$ $x<3$

If we start with $- 6 <$ $-6<$ $x + 3 < 6$ $x+3<6$ , we can begin by breaking this one expression into to, like so:

$- 6 <$ $-6<$ $x + 3$ $x+3$ and $x + 3 < 6$ $x+3<6$ . Now we can solve for the two different $x$ $x$ s.

$- 6 <$ $-6<$ $x + 3$ $x+3$ , minus $3$ $3$ on both sides, and we have $- 9 <$ $-9<$ $x$ $x$ .

With $x + 3 <$ $x+3<$ $6$ $6$ , we once again subtract $3$ $3$ on both sides, which leaves us with $x < 3$ $x<3$ .

So, $x$ $x$ can be greater than $- 9$ $-9$ and smaller that $3$ $3$ , which we can write as $- 9 <$ $-9<$ $x < 3$ $x<3$

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