To solve this inequality, first expand the terms on both sides of the equation:
(x+4)(x-2)-(x+5)(x+3) = x^2 - 2x + 4x - 8 - (x^2 + 3x + 5x + 15)
Now simplify the equation:
= x^2 - 2x + 4x - 8 - x^2 - 3x - 5x - 15= 2x - 23
Now compare this expression to the right side of the original inequality:
2x - 23 ≤ -8x
Add 8x to both sides:
10x - 23 ≤ 0
Add 23 to both sides:
10x ≤ 23
Divide by 10 on both sides to find the final solution:
x ≤ 2.3
Therefore, the solution to the original inequality is x ≤ 2.3.
To solve this inequality, first expand the terms on both sides of the equation:
(x+4)(x-2)-(x+5)(x+3) = x^2 - 2x + 4x - 8 - (x^2 + 3x + 5x + 15)
Now simplify the equation:
= x^2 - 2x + 4x - 8 - x^2 - 3x - 5x - 15
= 2x - 23
Now compare this expression to the right side of the original inequality:
2x - 23 ≤ -8x
Add 8x to both sides:
10x - 23 ≤ 0
Add 23 to both sides:
10x ≤ 23
Divide by 10 on both sides to find the final solution:
x ≤ 2.3
Therefore, the solution to the original inequality is x ≤ 2.3.