3|x-6| >= -2
Is this correct?
x>=16/3
x<=20/3
To find the solution for the inequality 3|x-6| >= -2, we need to follow a few steps:
Step 1: Remove the absolute value sign by considering two cases:
1. When x - 6 is positive or zero: In this case, the absolute value of x - 6 is equal to x - 6. So the inequality becomes 3(x - 6) >= -2.
2. When x - 6 is negative: In this case, the absolute value of x - 6 is equal to -(x - 6), which can be written as -x + 6. So the inequality becomes 3(-x + 6) >= -2.
Step 2: Simplify the inequalities separately:
Case 1: x - 6 ≥ 0 (when x - 6 is positive or zero)
3(x - 6) ≥ -2
3x - 18 ≥ -2
3x ≥ 16
x ≥ 16/3
Case 2: x - 6 < 0 (when x - 6 is negative)
3(-x + 6) ≥ -2
-3x + 18 ≥ -2
-3x ≥ -20
x ≤ 20/3
Step 3: Combine the solutions from both cases:
The solution to the inequality 3|x-6| >= -2 is:
x ≥ 16/3 (when x - 6 is positive or zero)
x ≤ 20/3 (when x - 6 is negative)
So your solution, x ≥ 16/3 and x ≤ 20/3, is correct.