We get that the solution for this inequalities will be x ≤ - 4.5.
We are given the inequalities:
- 2 x - 3 ≥ 6 or 3 ( x - 4 ) < - 6
For - 2 x - 3 ≥ 6:
Add 3 to both sides:
- 2 x - 3 + 3 ≥ 6 + 3
- 2 x ≥ 9
Divide both sides by - 2
- 2 x / - 2 ≤ 9 / - 2
x ≤ - 4.5
For 3 ( x - 4 ) < - 6:
Divide both sides by 3
x - 4 < - 6
Add 4 to both sides:
x - 4 + 4 < - 6 + 4
x < - 2
We get
x ≤ - 4.5 or x < -2
x will then be:
x ≤ - 4.5
Therefore, we get that the solution for this inequalities will be x ≤ - 4.5.
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