Question

Which represents the solution to the absolute value equation? 5|2x - 4| + 1 = 11?

Answer 1

A) x = 1 or x = 3
B) x = 1 or x = -3
C) x = 3 or x = - 3
D) x = 6 or x = 1

Answer 2

When 2x-4 >0 the equation becomes
5(2x-4)+1=11......(1)

when 2x-4<0 the equation becomes
-5(2x-4)+1=11 ........(2)

solve equation (1)& (2) for x

Answer 3

NOTE :-

|x|=x for x>0
|x|=-x for x<0

Answer 4

am i just trying to find a replacement number for x?

Answer 5

yes

Answer 6

okay, cause... 5(2x-4) + 1 = 11
2x - 4 = -2x
5(-2x)+ 1=11
-10x + 1 = 11
-9x = 11

Answer 7

right...?

Answer 8

so whatever x is has to get -9 up to 11?

Answer 9

im confused.

Answer 10

5(2x+4)+1=11
subtract 1 from both sides
5(2x+4)=10
divide 5 from both sides
(2x+4)=2
subtract 4 from both sides
2x=-2
divide by 2 both the side
x=-1

Answer 11

so u gt one solution for x as x=-1

Answer 12

The other equation is -5(2x-4)+1=11

solve it similarly

Answer 13

OHHHH I SEE...
-5(2x-4)+1=11
minus 1 both sides
-5(2x-4)=10
divide by -5 both sides
(2x-4) = -2
add 4 to both sides
(2x) = 2
divide by two
x = 1

Answer 14

i think...

Answer 15

@jiteshmeghwal9

Answer 16

Actually I wouldnt agree....you first need to get the absolute equation to itself....first you must get `1` to the other side...

\(\huge{5|2x-4|(1-1)=11-1}\)

What would that equal?

Answer 17

5|2x-4|=10

Answer 18

Correct :)

Now we have `5|2x-4|=10`....now since 5 is `by` `|2x-4|` that would mean we would divide to get it to the other side...so we divide by 5...

\(\huge{\frac{5}{5}|2x-4|=\frac{10}{5}}\)

What would that equal?

Answer 19

but i was correct though :P

Answer 20

|2x -4| = 2

Answer 21

Not quite x does not equal to -1...

Answer 22

Correct :) Now since this is a absolute equation the total can either be a positive or a negative sooo we would make two equation one with a positive total and one with a negative total....

\(\huge{2x-4=2}\)

\(\huge{2x-4=-2}\)

Do you understand?

Answer 23

seriously
there was a typo when i was solving my first equation

i solved 5(2x+4)+1=11 instead of 5(2x-4)+1=11

Answer 24

that's the reason behind why i gt x=-1 as my answer

Answer 25

Oooo I see then yea technically you were correct :P It just i didnt recognize with the absolute and real numbers on both sides....I was wondering why you didnt get the absolute to itself...@jiteshmeghwal9

Answer 26

@jiteshmeghwal9

Answer 27

Haha nvm that was my mistake

Answer 28

So we would simplify each equation to find x....

\(\huge{2x(-4+4)=(2+4)}\) We would subtract 4 from both sides....

Answer 29

Sorry I meant we would add by 4 to cancel out `-4`...my mistake

Answer 30

So we add it....

\(\huge{2x=6}\) Next to get the variable to itself we would divide by 2...

\(\huge{\frac{2x}{2}=\frac{6}{2}}\) What would that equal?

Answer 31

\[5\left| 2x-4 \right|+1=11,5\left| 2x+4 \right|=11-1=10\]
\[\left| 2x-4 \right|=\frac{ 10 }{ 5 }=2\]
\[2x-4=\pm 2\]
\[2x-4=2,2x=2+4=6,x=\frac{ 6 }{ 2 }=3\]
\[2x-4=-2,2x=-2+4=2,x=\frac{ 2 }{ 2 }=1\]