Question

( x − 1 ) ( x +2 ) ( x + 3 )<0

Answer 1

Х=1
х=-2
х=-3
__-__-3__+__-2__-__1___+___
(-&;-3)(-2;1)

Answer 2

To solve the inequality $(x - 1)(x + 2)(x + 3) < 0$, we need to find the intervals on the number line where the expression is negative.

We can approach this problem by analyzing the signs of each factor and determining the intervals in which the signs change.

Let's consider each factor separately:

1. $x - 1$: The sign changes at $x = 1$. It is negative for $x < 1$ and positive for $x > 1$.
2. $x + 2$: The sign changes at $x = -2$. It is negative for $x < -2$ and positive for $x > -2$.
3. $x + 3$: The sign changes at $x = -3$. It is negative for $x < -3$ and positive for $x > -3$.

Now, let's combine the information from these factors:

1. When $x < -3$, all three factors are negative. The product of three negative factors is negative.
2. Between $-3$ and $-2$, only the factor $x + 3$ is positive, while the other two factors are negative. The product of one positive and two negative factors is positive.
3. Between $-2$ and $1$, the factor $x + 2$ is positive, while the other two factors are negative. The product of one positive and two negative factors is negative.
4. For $x > 1$, all three factors are positive. The product of three positive factors is positive.

Therefore, the inequality $(x - 1)(x + 2)(x + 3) < 0$ is true when $x < -3$ or $-2 < x < 1$.

In interval notation, the solution is $(- \infty, -3) \cup (-2, 1)$.