Question

The sum of 3 integers is at most -34. If one integer is 27 and another is -35, which inequality represents the solution set for the third integer?

Answer 1

The solution set for the third integer is x < -26. The inequality that represents the solution set for the third integer, when the sum of three integers is at most -34 and two integers are 27 and -35, is x ≤ -26.

Step-by-step explanation:

The sum of 3 integers is at most -34. If one integer is 27 and another is -35, the inequality that represents the solution set for the third integer is x < -34 - 27 - (-35). Simplifying the inequality, we get x < -34 - 27 + 35 = -34 + 8 = -26.

The inequality that represents the solution set for the third integer, when the sum of three integers is at most -34 and two integers are 27 and -35, is x ≤ -26.

The student is asking for the inequality that represents the solution set for the third integer, given that the sum of 3 integers is at most -34, and two of the integers are already provided (27 and -35).

Since we know that the sum of the three integers must be ≤ -34, and we already have two of the integers, we can set up the inequality to find the third integer (let's call it x):

27 + (-35) + x ≤ -34

Simplifying this, we have:

-8 + x ≤ -34

To isolate x, subtract -8 from both sides of the inequality:

x ≤ -34 + 8

x ≤ -26

So, the inequality that represents the solution set for the third integer is x ≤ -26.