This means our returns would be between $400 and $800.
To solve absolute value inequalities, just as with absolute value equations, we write two inequalities and then solve them independently.
Absolute value inequalities
For an algebraic expression
X, and
an
absolute value inequality is an inequality of the form
These statements also apply to
and
Determining a number within a prescribed distance
Describe all values
within a distance of 4 from the number 5.
We want the distance between
and 5 to be less than or equal to 4. We can draw a number line, such as in
[link], to represent the condition to be satisfied.
The distance from
to 5 can be represented using an absolute value symbol,
Write the values of
that satisfy the condition as an absolute value inequality.
We need to write two inequalities as there are always two solutions to an absolute value equation.
If the solution set is
and
then the solution set is an interval including all real numbers between and including 1 and 9.
Using a graphical approach to solve absolute value inequalities
Given the equation
determine the
x -values for which the
y -values are negative.
We are trying to determine where
which is when
We begin by isolating the absolute value.
Next, we solve for the equality
Now, we can examine the graph to observe where the
y- values are negative. We observe where the branches are below the
x- axis. Notice that it is not important exactly what the graph looks like, as long as we know that it crosses the horizontal axis at
and
and that the graph opens downward. See
[link].
Interval notation is a method to indicate the solution set to an inequality. Highly applicable in calculus, it is a system of parentheses and brackets that indicate what numbers are included in a set and whether the endpoints are included as well. See
[link] and
[link].
Solving inequalities is similar to solving equations. The same algebraic rules apply, except for one: multiplying or dividing by a negative number reverses the inequality. See
[link],[link] ,
[link] , and
[link].
Compound inequalities often have three parts and can be rewritten as two independent inequalities. Solutions are given by boundary values, which are indicated as a beginning boundary or an ending boundary in the solutions to the two inequalities. See
[link] and
[link] .
Absolute value inequalities will produce two solution sets due to the nature of absolute value. We solve by writing two equations: one equal to a positive value and one equal to a negative value. See
[link] and
[link].
Absolute value inequalities can also be solved by graphing. At least we can check the algebraic solutions by graphing, as we cannot depend on a visual for a precise solution. See
[link] .
Evolution models refer to mathematical and computational representations of the processes involved in biological evolution. These models aim to simulate and understand how species change over time through mechanisms such as natural selection, genetic drift, and mutation. Evolutionary models can be u
faruk
what are the modern trends in religious behaviours
shared standards of acceptable behavior by the group or appropriate behavior in a particular institution or those behaviors that are acceptable in a society
Lucius
that is how i understood it
Lucius
examples of societal norms
Diamond
Discuss the characteristics of the research located within positivist and the interpretivist paradigm
