Question

Solve 2|5x − 2| + 4 = 18 for x. Show your work to receive full credit.

Answer 1

first, subtracted by 4 to both sides, giving us
2|5x − 2| + 4 - 4 = 18 - 4
2|5x − 2| = 14

Answer 2

then divided by 2 to both sides :
2|5x − 2|/2 = 14/2
|5x − 2| = 7

Answer 3

now, if given an equation |f(x)| = c, with c a constant
then the solution satisfies when f(x) = c or -f(x) = c

Answer 4

so, if given an equation |5x − 2| = 7, its solution is
5x − 2 = 7 or
-(5x − 2) = 7
solve for x

Answer 5

case I :
5x − 2 = 7
added by 2 to both sides :
5x -2 +2 = 7+2
5x = 9
divided by 5,
5x/5 = 9/5
x =9/5

Answer 6

case II :
-(5x − 2) = 7
multiply by -1 to both sides :
-(5x − 2)(-1) = 7(-1)
5x − 2 = -7
added by 2 to both sides :
5x - 2 + 2 = -7 + 2
5x = -5
divided by 5 to both sides :
5x/5 = -5/5
x = -1

Answer 7

so, the solution is {-1, 9/5}

Answer 8

THANK YOU! THANK YOU! THANK YOU!
I tried solving this problem & failed but thank you for helping me and using your time to help me with this!!! :)

Answer 9

very welcome ::)