Answer:
There are generally 3 methods to solve inequalities
Explanation:
By algebraic method
Example 1: Solve: 2x - 7 < x - 5
2x - x < 7 - 5
x < 2
By the number-line method.
Example 2. Solve
f
(
x
)
=
x
2
+
2
x
−
3
<
0
First, solve f(x) = 0. There are 2 real roots x1 = 1, and x2 = - 3.
Replace x = 0 into f(x). We find f(0) = - 3 < 0. Therefor, the origin O is located inside the solution set.
Answer by interval: (- 3, 1)
--------------------- - 3 ++++++++ 0 ++++ 1 ----------------
3.By graphing method.
Example 2. Solve:
f
(
x
)
=
x
2
+
2
x
−
3
<
0
.
The graph of f(x) is an upward parabola (a > 0), that intersects the x-axis at x1 = 1 and x2 = - 3. Inside the interval (-3, 1), the parabola stays below the x-axis --> f(x) < 0.
Therefor, the solution set is the open interval (-3, 1)
graph{x^2 + 2x - 3 [-10, 10, -5, 5]}