Trouble with absolute value!!! Pleaz help.?

Question

I do not understand how to solve the following equation. I hope that u guys can understand this:

solve: absolute value of 3 - 3/4x=1/4?

Somebody please help me and give explanation as to how the problem is done! Much thanks.

Answer 1

solve: absolute value of 3 - 3/4x=1/4?

first I put it into "familiar notation for me ... something like:


{{ using the "|" brackets to emulate "abs val" }}


| 3 - 3/4x | = 1/4 ... then I'd multply both sides by 4 ...
4 * | 3 - 3/4x | = 4 * 1/4
| 12 - 3 / x| = 1

hmmm, next I'd multply both sides by x (I should have combined this with the earlier step, but "typing" isn't conducive to "math-thinnking" habits ... much easier with pencil & paper ...


x * | 12 - 3 / x| = 1 * x

| 12x - 3 | = x ... at this point break it into two "cases"

case (a)
x = (12x - 3)

and

case(b)
x = - (12x - 3)

/*************************/
case (a)
x = 12x - 3
-11x = -3
x = 3/11


case(b)
x = - (12x - 3)
x = -12x + 3 [note the "sign-change on "3"]
13x = 3
x = 3 / 13

/*************************/
so ...
x = 3 / 13 and x = 3 / 11 are both solutions:

/*************************/

to "check" replace in the original eqn:
| 3 - 3/4x | = 1/4
| 3 - 3 / (4*(3/11)) | = 1/4
| 3 - 1 / (4/11) | = 1/4
|3 - 11/4| = 1/4
| 12/4 - 11/4| = 1/4
|1/4| = 1/4
1/4 = 1/4
ok


case(b)
| 3 - 3/4x | = 1/4
| 3 - 3 / (4* 3/13) | = 1/4
|3 - 1/(4/13) | = 1/4
|3 - 13/4| = 1/4
|12/4 - 13/4| = 1/4
|-1/4| = 1/4
1/4 = 1/4
ok

Answer 2

since the absolute value of that is equal to 1/4 then the value inside the absolute value signs (3-3/4x) can either equal positive 1/4 or negative 1/4.

so set that expression (3-3/4x) equal to 1/4 and then solve for x. and then set that expression (3-3/4x) equal to -1/4 (negative 1/4) and solve for x.

i'm not sure if you mean (3/4)x or 3/(4x) so i couldnt find the answer for you but the method described above is the way u do it

Answer 3

just do the problem like normal. absolute value is like: 2-3=-1 the absolute value is 1. the absolute of any negative # is it's positive. and the abs val of a pos is it's itself. if the number looks like this |-4| u need the absolute value of neg 4 which is 4. confused? hope not. 3 minus 3/4 = 2 1/4 so 2 times what equals 1/4? 2.67. i'm pretty sure, i havn't done that in like 2 years though.

Answer 4

well, the absolute value of a number is the distance between that number from 0 on a number line, so the absolute value of 3 is 3. then you subtract 3 from the left side and right side, so you can divide to find the value of x. (i did it- and got -3 and 2/3 as an answer but im not in algebra this year)

Answer 5

Solve like other algebra variable question.
If you need the answer, it's 11/3, or 3 and 2/3.

Answer 6

3 - 3/4x=1/4
-3/4x = 1/4 - 3
-3/4x = 11/4
x = 11/4 : -3/4
x = 11/4 . -4/3
x = -11/3
Solution: {x is element of R| x = -11/3}
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Answer 7

if by this you mean

|3 - (3/4)x| = (1/4)

This can be the same as saying

±(3 - (3/4)x) = (1/4)
3 - (3/4)x = (±1/4)
12 - 3x = ±1
-3x = -11 or -13
x = (11/3) or (13/3)

ANS : x = (11/3) or (13/3)

Answer 8

problem has nothing to do with absolute value

3 - (3/4)*x =1/4
12-3x=1
3x=11
x=11/3
if problem is 3-3/(4x)=1/4
12x-3=x
11x=3

x=3/11

Answer 9

It is solved like any other algebra question. Isolate and solve for x.

Answer 10

abs x= sqrt((x)^2)