There are three types
of open sentences that can involve absolute value. They are listed below. Note
that in each case, n is nonnegative since the absolute value of a number
can only equal 0 or a positive number.
You
have already studied equations involving absolute value. Inequalities involving
absolute value are similar. Consider the graphs and solutions of the three open
sentences below.
For both equations and inequalities
involving absolute value, there are two cases to consider.
Case 1 The value within the absolute value symbols is
positive.
Case 2 The value within the absolute value symbols is
negative.
1.
Solve │x – 5│≤ 2. Graph the solution.
Alternative Solutions:
So,
the solution is {x│3 ≤ x ≤ 7}.
The solution makes sense
since 3 and 7 are at most 2 units from 5.
As in Example 1, when solving an inequality involving absolute value and the symbols < or ≤, the solution can be written as an inequality using and. However, when solving an inequality involving absolute value and the symbols > or ≥, the solution can be written as an inequality using or.
Example
2.
Solve │6x│> 18. Graph the solution.
Alternative Solutions:
So,
the solution is {x│x
< –3 or ≤
x > 3}.
Inequalities
involving absolute value are often used to indicate tolerance. Tolerance
is the amount of error or uncertainty that is allowed when taking measurements.
Measurement Link
3.
When producing ½ -inch bolts for bicycle parts, the tolerance is 0.005
inch. What is the range of acceptable bolt measures?
Alternative Solutions:
Sumber
Thanks for reading Solving Inequalities Involving Absolute Value. Please share...!
