Question

Solve for x. put your answer in interval notation using grouping symbols
x^2+6x<0

Answer 1

To solve a polynomial inequality do this:
1. change the inequality sign to an equal sign and solve the equation.
2. plot each solution to the equation on a number line.
3. the number line is now divided into regions.
4. test a point from each region in the original inequality.

Answer 2

You lost me at step 3

Answer 3

Let's say an equation has the roots -2 and 6.
You plot them as shown above.

Answer 4

There are three regions in the number line.
You can call them intervals.
\((-\infty, -2)\), \((-2, 6)\), \((6, \infty)\),

Answer 5

Now you test a point from each interval in the original inequality.
If the point works in the original inequality, then that entire interval works and is part of the solution.

Answer 6

\[x^2+6x<0\]
add 9 to both sides of enequality
\[x^2+6x+9<9\]
\[\left( x+3 \right)^2<3^2\]
\[\left| x+3 \right|<3\]
-3<x+3<3
-6<x<0