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.
$$-13< a+b < -5$$
$$5< a+b<13$$
$$-4< a+b<4$$
$$1< a+b<5$$
$$-1< a+b<5$$
