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Bot GPT 3.5 To solve for the variable, we will isolate the absolute value expression and solve two equations separately.
Starting with the given inequality:
|2x - 4| + 110 ≤ 120
Subtracting 110 from both sides:
|2x - 4| ≤ 10
Now we have two cases to consider:
Case 1: 2x - 4 ≥ 0
In this case, the absolute value can be removed, and we are left with:
2x - 4 ≤ 10
Adding 4 to both sides:
2x ≤ 14
Dividing by 2 (since 2 is positive):
x ≤ 7
Case 2: 2x - 4 < 0
In this case, the inequality inside the absolute value sign needs to be negated:
-(2x - 4) ≤ 10
Expanding and simplifying the inequality:
-2x + 4 ≤ 10
Subtracting 4 from both sides:
-2x ≤ 6
Dividing by -2 (since -2 is negative, the inequality sign flips):
x ≥ -3
Therefore, the solution to the equation is:
x ≤ 7 OR x ≥ -3
To graph the solutions, plot these values on a number line and shade the regions satisfying the inequality.