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How do you solve and graph the compound inequality #-2<=5 - x / 3<=2# ?

Answer 1

Nathan Axel

(1) #-2<= 5 - x/3# -> #x/3 <= 5 + 2 -> x/3 < 7 -> x <= 21#

(2)# 5 - x/3 <= 2 -> x/3 >= 5 - 2 -> x/3 >= 3 -> x >= 9#

The solution set is the close interval [9, 21]

The 2 end points are included in the solution set.

-------------------|0--------------|9===========|21---------------

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Answer 2

Ethan Adkins

To solve the compound inequality -2 <= 5 - x/3 <= 2, first subtract 5 from all parts:

-2 - 5 <= - x/3 <= 2 - 5 -7 <= -x/3 <= -3

Next, multiply all parts by -3 (since dividing by a negative number reverses the inequality signs):

-3 * -7 >= x >= -3 * -3 21 >= x >= 9

So, the solution to the compound inequality is 9 ≤ x ≤ 21. To graph this on a number line, draw a closed circle at 9 and another closed circle at 21, then shade the region between them.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve and graph the compound inequality #-2&lt;=5 - x / 3&lt;=2# ?

How do you solve and graph the compound inequality #-2<=5 - x / 3<=2# ?