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# Inequalities: Simultaneous Inequalities

If $$-7 < a < -2$$ and $$18 > -3b > 9$$, which of the following inequalities gives all of the possible values of $$a+b$$?
Correct. [[Snippet]] The $$-3b$$ gets in the way of reaching the desired result of $$a + b$$. Divide the second inequality by $$-3$$. Don't forget to flip the sign. >$$\frac{18}{-3} > \frac{-3b}{-3} > \frac{9}{-3}$$ >$$-6 < b < -3$$ Now, line the inequalities up so that the sign goes in the same direction. >$$-7 < a < -2$$ >$$-6 < b < -3$$ Finally, add the inequalities. >$$-13 < a + b < -5$$ Hence, this is the correct answer.

Incorrect.

[[Snippet]]

Did you forget to flip the inequality signs after multiplication/division by a negative number? Remember to flip the inequality sign every time you multiply or divide by a negative number.
Incorrect. [[snippet]] Carefully check your calculations.
Incorrect. [[snippet]] Carefully check your work.
Incorrect. [[snippet]] You might have gotten this answer if you made a sign error in your calculations.
$$-13< a+b < -5$$
$$5< a+b<13$$
$$-4< a+b<4$$
$$1< a+b<5$$
$$-1< a+b<5$$