Question

Solve the inequality. Graph the solutions.
StartAbsoluteValue 4 x minus 5 EndAbsoluteValueplus5greater than8
Question content area bottom
Part 1
Select the correct choice below and fill in any answer boxes in your choice.
A.
The solution is
  
enter your response hereless thanxless than
  
enter your response here. ​(Type integers or simplified​ fractions.)
B.
The solution is xequals
  
enter your response here. ​(Type an integer or a simplified​ fraction.)
C.
The solution is xless than
  
enter your response here or xgreater than
  
enter your response here. ​(Type integers or simplified​ fractions.)
D.
The solution is all real numbers.
E.
There is no solution.

Answer 1

|4x - 5| + 5 > 8
⇒ |4x - 5| > 3.

Solve:
4x - 5 > 3 ⇒ 4x > 8 ⇒ x > 2.
or
4x - 5 < -3 ⇒ 4x < 2 ⇒ x < 1/2.

So the solution is x < 1/2 or x > 2 (option C).

Graph: (-∞, 1/2) ∪ (2, ∞) — open circles at 1/2 and 2, shading to the left of 1/2 and to the right of 2.