Respuesta :
[tex]x > - 5[/tex] or [tex]x < 10[/tex] are the two possible solutions to the given inequality.
What are absolute value functions?
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
What is inequality?
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.
According to the given question.
We have an inequality |3x| > x + 20
Solve the above given inequality |3x| > x + 20
⇒ [tex]-(x + 20) < 3x < +( x + 20)[/tex]
⇒ [tex]-x -20 < 3x < x + 20[/tex]
⇒ [tex]3x > -x -20[/tex] or [tex]3x < x + 20[/tex]
⇒ [tex]3x+x > -20[/tex] or [tex]3x - x < 20[/tex]
⇒ [tex]4x > -20[/tex] or [tex]2x < 20[/tex]
⇒[tex]x > -5[/tex] or [tex]x < 10[/tex]
⇒ x ∈ (-∞, -5)∪(10,∞)
Hence, [tex]x > - 5[/tex] or [tex]x < 10[/tex] are the two possible solutions to the given inequality.
Find out more information about absolute value inequalities here:
https://brainly.com/question/27517767
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