Question

solve absolute value inequality. 4|x-7|-6≤14

Answer 1

4|x-7|-6≤14
4|x-7|≤20
|x-7| <= 5
x-7<= 5 or x-7<= -5
x<=12 or x<=2

Answer 2

how did you get 20?

Answer 3

4|x-7|-6≤14
add 6 to both sides
4|x-7|≤20

Answer 4

devide both sides by 4
|x-7| <= 5

Answer 5

why do you divide by 4?

Answer 6

cuz i see 4|x-7|≤20
and i want to isolate x eventually
therfore im interested in |x-7| on the left side.

Answer 7

i have 4 * |x-7| on the left side...im only interested in |x-7|
so i hav to devide the left side by 4...since we devide the left side by 4, we HAVE to devide the right side by 4

Answer 8

ok, i see. how did you get x-7≤ 5 or x-7≤ -5? how'd you get the -5?

Answer 9

by definition, if |x| = A
x = A or x = -A

Answer 10

cuz when u take the absolute value of A, it is A
and when u take the absolute value of -A, it is A

This 'A' can be any real number

Answer 11

so theres two answers then? x≤12 and x≤2

Answer 12

yes. x≤12 OR x≤2

Answer 13

ok, if i was to graph the solution, how would i?

Answer 14

i drew a line at x=2, the red vertival line..and just shaded the area (that is left side in this case) x<=2

Answer 15

do the same for x<=12
draw a line at x=12, and shade the less than area, that is left side

Answer 16

ok, i see. thank you.

Answer 17

I think that is wrong^ :|

Answer 18

|x-7|<=5

-5<= (x-7) <= 5

2<= x <= 12 CORRECT

that is different from the other person answer

Answer 19

also, if the answer was x<=12 or x<=2 then you would merge both the solutions to just x<=12, bec ause that is where they both hold, BUT REMEMBER THAT ANSWER IS INCORRECT , corrrect answer is above

Answer 20

EDIT: you would merge them to x<=2

Answer 21

thanks