To solve the inequality (x+5)/(x-4) ≥ (x-12)/(x+3), we can start by finding a common denominator for both fractions.
First, cross multiply to get rid of the denominators:(x+5)(x+3) ≥ (x-12)(x-4)
Expanding both sides:x^2 + 3x + 5x + 15 ≥ x^2 - 4x - 12x + 48
Simplify each side:x^2 + 8x + 15 ≥ x^2 - 16x + 48
Subtract x^2 from both sides to get:8x + 15 ≥ -16x + 48
Add 16x to both sides:24x + 15 ≥ 48
Subtract 15 from both sides:24x ≥ 33
Divide by 24:x ≥ 33/24x ≥ 11/8
Therefore, the solution to the inequality is x ≥ 11/8.
To solve the inequality (x+5)/(x-4) ≥ (x-12)/(x+3), we can start by finding a common denominator for both fractions.
First, cross multiply to get rid of the denominators:
(x+5)(x+3) ≥ (x-12)(x-4)
Expanding both sides:
x^2 + 3x + 5x + 15 ≥ x^2 - 4x - 12x + 48
Simplify each side:
x^2 + 8x + 15 ≥ x^2 - 16x + 48
Subtract x^2 from both sides to get:
8x + 15 ≥ -16x + 48
Add 16x to both sides:
24x + 15 ≥ 48
Subtract 15 from both sides:
24x ≥ 33
Divide by 24:
x ≥ 33/24
x ≥ 11/8
Therefore, the solution to the inequality is x ≥ 11/8.