Question

Solve the absolute value inequality: |x - 4| > 2

Answer 1

there are two solution to absolute so
x-4>2
x-4>-2
solving first
x=6
solving the second
x=2

Answer 2

Which way do the signs go?

Answer 3

This will form two equations:

first one is:

\[x - 4 > 2\]

and second one will be:

\[-(x-4) > 2 \implies x - 4 < -2\]

Answer 4

Actually, the two equations are
x-4 > 2
and
x-4 < -2

So the answer would be
x>6 and x<2

Answer 5

Solve for x in both the equations..

Answer 6

So how would you do this one : Solve the absolute value inequality: |2x - 3| < 7
?

Answer 7

actually actually the two solutions will be \(x<0 \text{ or } x>6\)

Answer 8

Follow the same procedure as anemonix did.. @reneebbyx3

Answer 9

I don't get it how she did it though.

Answer 10

when you have an absolute value equation or inequality, you must remove the absolute value to solve
when you remove the absolute value, you will get two separate equations or inequalities to solve

Answer 11

@anemonix she did not get what you explained..

Can you explain it more to @anemonix

Answer 12

for example to solve \(|2x-3|<5\) you must solve
\[-5<2x-3<5\]

Answer 13

there are two possible solutions
one is
2x-3<7
second one is
2x-3<-7

solving the first one
add three two both sides
2x>7+3
2x>=10
divide both sides by 2
x>5

for second one
2x-3>-7
add three on both sides
2x>-7+3
2x>-4
or invert it
2x<4
divide by 2 both sides
x=<2

Answer 14

\[-2 < x-4 < 2 \implies 2<x<6\]

How did you get < 0 @satellite73

Answer 15

I used the same method that @satellite73 used, except I got the same answer that @waterineyes got.

When solving for |x-4| >2
You split it into -2>x-4>2
By adding 4 to both sides, you get 2>x>6, or x<2 and x >6.

Answer 16

I think he found it taking the derivative, minima and maxima whatever the terms are..

Answer 17

As for your second question: |2x - 3| < 7
You can split this into -7<2x-3<7
First, you add 3 to both sides to get: -4<2x<10
Then you divide both sides by 2: -2<x<5, so your answer would be x>-2 and x<5

Answer 18

I got it now. Thank you.

Answer 19

But we are in doubt now..

Ha ha ha..