Question

A) (x + 8)(x - 5) > 0;​

Answer 1

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Answer 2

To solve the inequality $(x + 8)(x - 5) > 0$, you can use the concept of sign analysis. The idea is to find the intervals on the number line where the expression is positive.

First, let's find the critical points where the expression $(x + 8)(x - 5)$ equals zero:

1. Set $x + 8 = 0$: $x = -8$

2. Set $x - 5 = 0$: $x = 5$

Now, we have three intervals to consider: $x < -8$, $-8 < x < 5$, and $x > 5$.

1. For $x < -8$, both $x + 8$ and $x - 5$ are negative, so their product is positive. Thus, $(x + 8)(x - 5) > 0$ for $x < -8$.

2. For $-8 < x < 5$, $x + 8$ is positive, but $x - 5$ is negative. The product of a positive and a negative number is negative. Thus, $(x + 8)(x - 5) < 0$ for $-8 < x < 5$.

3. For $x > 5$, both $x + 8$ and $x - 5$ are positive, so their product is positive. Thus, $(x + 8)(x - 5) > 0$ for $x > 5$.

So, the solution to the inequality $(x + 8)(x - 5) > 0$ is:

$x < -8 \quad \text{or} \quad x > 5$