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.

$$-13< a+b < -5$$

$$5< a+b<13$$

$$-4< a+b<4$$

$$1< a+b<5$$

$$-1< a+b<5$$