Multi-Step Inequalities

Add yours

Sorry, we don't have any videos for this topic yet.
Let teachers know you need one by requesting it

Log in so we can tell you when a lesson is added.

Key Questions

  • Answer:

    Inequalities are very tricky.

    Explanation:

    When solving a multi step equation, you use PEMDAS (parentheses, exponents, multiplication, division, add, subtract), and you also use PEMDAS when solving a multi step inequality. However, inequalities are tricky in the fact that if you multiply or divide by a negative number, you must flip the sign. And while normally there are 1 or 2 solutions to a multi step equation, in the form of x= #, you'll have the same thing, but with an inequality sign (or signs).

  • I would start with arranging terms so that all variables are on one side.


    I hope that this was helpful.

  • Answer:

    #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]}

  • Suppose we're solving in #\mathbb{R}#

    #0x=1 \Rightarrow S = \emptyset#

    #0x=0 \Rightarrow S = \mathbb{R}#

Questions