Question

Determine the largest integer value of x in the solution of the following inequality.

3x - 6 ≤ -14

Answer 1

The largest integer value for x satisfying the inequality 3x - 6 ≤ -14 is -3. This was found by isolating x and finding the greatest integer less than or equal to -2.666...

Step-by-step explanation:

To determine the largest integer value of x in the inequality 3x - 6 ≤ -14, first solve the inequality.

1. Add 6 to both sides of the inequality to isolate the term with x:
   
   3x - 6 + 6 ≤ -14 + 6
   
   3x ≤ -8
2. Divide both sides by 3 to solve for x:
   
   3x / 3 ≤ -8 / 3
   x ≤ -2.666...
3. Since we need the largest integer value of x, and integers are whole numbers, the largest integer less than or equal to -2.666... is -3.

Therefore, the largest integer value for x satisfying the inequality 3x - 6 ≤ -14 is -3.

Answer 2

3x <= -8

x<= -8/3 means smaller or equal -8/3

->-8/3