The given inequalities are:
1) x - 4 < 8 ÷ (2x + 5)
2) 8 ÷ (2x + 5) < 13 ÷ (3 - x)
3) 13 ÷ (3 - x) > 1
To solve these inequalities, we can simplify each one individually:
1) x - 4 < 8 ÷ (2x + 5x - 4 < 4 / (x + 2.5(x - 4)(x + 2.5) < x^2 - 1.5x - 10 < (x - 2)(x + 5) < -5 < x < 2
2) 8 ÷ (2x + 5) < 13 ÷ (3 - x8 / (2x + 5) < 13 / (3 - x8(3 - x) < 13(2x + 524 - 8x < 26x + 60 < 34x + 4-41/34 < x
3) 13 ÷ (3 - x) > 13 / (3 - x) > 13 > 3 - x > -10
Combining the solutions of the three inequalities, we get:
-10 < x < -5
Therefore, the solution set for x is -10 < x < -5.
The given inequalities are:
1) x - 4 < 8 ÷ (2x + 5)
2) 8 ÷ (2x + 5) < 13 ÷ (3 - x)
3) 13 ÷ (3 - x) > 1
To solve these inequalities, we can simplify each one individually:
1) x - 4 < 8 ÷ (2x + 5
x - 4 < 4 / (x + 2.5
(x - 4)(x + 2.5) <
x^2 - 1.5x - 10 <
(x - 2)(x + 5) <
-5 < x < 2
2) 8 ÷ (2x + 5) < 13 ÷ (3 - x
8 / (2x + 5) < 13 / (3 - x
8(3 - x) < 13(2x + 5
24 - 8x < 26x + 6
0 < 34x + 4
-41/34 < x
3) 13 ÷ (3 - x) >
13 / (3 - x) >
13 > 3 -
x > -10
Combining the solutions of the three inequalities, we get:
-10 < x < -5
Therefore, the solution set for x is -10 < x < -5.