Here is the problem:
7 + 4x > 18 – 6(x + 5)
First, let's simplify the right side of the inequality:
18 - 6(x + 5) = 18 - 6x - 30
= -6x - 12
So the inequality becomes:
7 + 4x > -6x - 12
Now, let's move all the x terms to one side and the constant terms to the other side. Add 6x to both sides:
7 + 4x + 6x > -12
7 + 10x > -12
Subtract 7 from both sides:
10x > -12 - 7
10x > -19
Finally, divide by 10:
x > -19 / 10
x > -1.9
The solution in interval notation is (-1.9, +∞).
Let's check the options:
1) (-∞; 1,9)
2) (1,9; +∞)
3) (-∞; -1,9)
4) (−1,9; +∞)
The correct option is 4.