Solve the first inequality: (x+8)(x-5) > 0 Make a sign analysis chart:
In the interval (-∞, -8), both factors are negative, so the product is positive. In the interval (-8, 5), the first factor is positive and the second factor is negative, so the product is negative. In the interval (5, ∞), both factors are positive, so the product is positive.
Therefore, the solution to (x+8)(x-5) > 0 is x < -8 or x > 5.
Solve the second inequality: (x-14)(x+10) < 0 Make a sign analysis chart:
In the interval (-∞, -10), both factors are negative, so the product is positive. In the interval (-10, 14), the first factor is negative and the second factor is positive, so the product is negative. In the interval (14, ∞), both factors are positive, so the product is positive.
Therefore, the solution to (x-14)(x+10) < 0 is -10 < x < 14.
Combining both inequalities, the solution is: -10 < x < 14.
To solve the inequalities:
Solve the first inequality: (x+8)(x-5) > 0Make a sign analysis chart:
In the interval (-∞, -8), both factors are negative, so the product is positive.
In the interval (-8, 5), the first factor is positive and the second factor is negative, so the product is negative.
In the interval (5, ∞), both factors are positive, so the product is positive.
Therefore, the solution to (x+8)(x-5) > 0 is x < -8 or x > 5.
Solve the second inequality: (x-14)(x+10) < 0Make a sign analysis chart:
In the interval (-∞, -10), both factors are negative, so the product is positive.
In the interval (-10, 14), the first factor is negative and the second factor is positive, so the product is negative.
In the interval (14, ∞), both factors are positive, so the product is positive.
Therefore, the solution to (x-14)(x+10) < 0 is -10 < x < 14.
Combining both inequalities, the solution is: -10 < x < 14.