|2x+7|<=27
For |2x+7| to be less than or equal to 27, we can split the inequality into two separate cases:
1. When (2x+7) is positive:
In this case, the inequality becomes:
2x + 7 ≤ 27
Subtracting 7 from both sides:
2x ≤ 20
Dividing both sides by 2:
x ≤ 10
2. When (2x+7) is negative:
In this case, the inequality becomes:
-(2x + 7) ≤ 27
Multiplying both sides by -1 (which reverses the inequality):
2x + 7 ≥ -27
Subtracting 7 from both sides:
2x ≥ -34
Dividing both sides by 2:
x ≥ -17
Combining both cases:
x ≤ 10 or x ≥ -17
To solve the inequality |2x + 7| ≤ 27, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 2x + 7 ≥ 0
Solving this inequality, we have:
2x + 7 ≤ 27
2x ≤ 27 - 7
2x ≤ 20
x ≤ 20/2
x ≤ 10
Case 2: 2x + 7 < 0
Solving this inequality, we have:
-(2x + 7) ≤ 27
2x + 7 ≥ -27
2x ≥ -27 - 7
2x ≥ -34
x ≥ -34/2
x ≥ -17
Thus, the solution to the inequality |2x + 7| ≤ 27 is x ≤ 10 or x ≥ -17.