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# Inequalities: Simultaneous Inequalities

If $$12 > a > 5$$ and $$9 > -b > 2$$, which of the following inequalities gives all possible values of $$a+b$$?
Correct. [[Snippet]] >$$9 \cdot (-1) < -b \cdot (-1) < 2 \cdot (-1)$$ >$$-9 < b < -2$$ Now, line the inequalities up so that the sign goes in the same direction. >$$12 > a > 5$$ >$$-2 > b > -9$$ Finally, add the inequalities. >$$10 > a + b > -4$$ Hence, this is the correct answer.
Incorrect. [[Snippet]] Carefully check your work.
Incorrect. [[Snippet]] Carefully check your calculations.
Incorrect. [[Snippet]] You might have gotten this answer if you made a sign error when finding the answer.
Incorrect. [[Snippet]] Carefully check your work.
$$-10 < a+b <4$$
$$4 < a+b < 10$$
$$-10 < a+b < -4$$
$$-4 < a+b < 10$$
$$-4 < a+b < 4$$