First, let's isolate the absolute value expression by subtracting 9 from both sides:
-|2x + 7| ≤ 6 - 9
-|2x + 7| ≤ -3
Next, let's remove the negative sign by multiplying through by -1:
|2x + 7| ≥ 3
Now, we can split the absolute value into two separate cases:
Case 1: (2x + 7) ≥ 3
2x + 7 ≥ 3
2x ≥ -4
x ≥ -2
Case 2: -(2x + 7) ≥ 3
-2x - 7 ≥ 3
-2x ≥ 10
x ≤ -5
Therefore, the solution to the inequality is x ≤ -5 or x ≥ -2, which can be expressed using interval notation as (-∞, -5] ∪ [-2, ∞).
Solve the absolute value inequality. Express the answer using interval notation.
9 − |2x + 7| ≤ 6
1 answer