please help me out with this equation Solve 4x Select the co

please help me out with this equation.

Solve 4x Select the correct choice below and fill in any answ A. The solution set is Simplify your answer. Use a comma to se OR, The solution set is the empty set

Solution

Solution : |a | = a when a>=0 and |a| = - a when a<=0

using the definition of mod function we have | 4x - 1| = 4x - 1 whem 4x - 1 >=0 ie x>=1/4

|4x -1| = - ( 4x - 1) when x <= 1/4

redefining the fn : 4x - 1 = 6 when x >=1/4 ===> 4x = 7 and x= 7/4 which is >1/4 Ans x =7/4

1 - 4x = 6 when x<= 1/4 , - 4x = 5 and x= - 5/4 which is <1/4 Ans x = -5/4

2 solutions which satisfy the eqn are x = 7/4 and - 5/4