Question

How do you solve multi step inequalities?

Answer 1

#There are generally 3 methods to solve inequalities

Explanation:

We can usually solve inequalities by 3 ways:

1. By algebraic method
   Example 1: Solve: 2x - 7 < x - 5
   2x - x < 7 - 5
   x < 2
2. By the number-line method.
   Example 2. Solve `f(x) = x^2 + 2x - 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 + 2x - 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]}