Respuesta :
The solution in set-builder notation is B. {x : −5 < x < 6}
The solution in interval notation is C. (–5, 6)
What is an absolute value?
Absolute value refers to the distance of a number from zero, regardless of direction. The distance is always positive, as absolute value of a number cannot be negative.
What is Set Builder Notation?
Set-builder notation is defined as a representation or a notation that can be used to describe a set that is defined by a logical formula that simplifies to be true for every element of the set. The set builder notation includes one or more than one variables.
What is Interval Notation?
Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.
What is an inequality?
Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Remove the absolute value term. This creates a ± on the right side of the inequality because
[tex]|x|=\pm x\\\\|2x-1| < \pm11[/tex]
Set up the positive portion of the ± solution.
2x - 1 < 11
Solve the first inequality for x.
[tex]2x-1 < 11\\\\2x < 12\\\\x < 6[/tex]
Set up the negative portion of the ± solution.
When solving the negative portion of an inequality, flip the direction of the inequality sign.
2x - 1 > -11
Solve the second inequality for x.
[tex]2x-1 > -11\\\\2x > -10\\\\x > -5[/tex]
Set up the intersection for the inequalities.
x < 6 and x > -5
Find the intersection between the inequalities.
−5<x<6
Convert the inequality to interval notation (−5,6)
In set builder form, {x : −5 < x < 6}
For more information on inequalities: https://brainly.com/question/20383699
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