Absolute value problem?

Question

|y|-6=2

my book says the solution is y=4 or y=-4

how is it both??

another problem says |m|+1=-7.

solution: |m|= -8

why isn't it |m|=8 or |m|=-8 like the other one?

how do you know when it's both or one?

Answer 1

The absolute value is the distance away from zero on a number line. So the -6 is 6 places away from 0 so the abssolute value of -6 is 6.

Then |m|+1=-7 is -8 because 8+1 does not equal -7 it equals 9.

Answer 2

The absolute value is defined as the positive value of the results of what is inside the bars. |a| = |-a|

if a is 5 then |5| = 5, if a is -5 then |-5| = 5

Solving the first equation for |y| by adding 6 to both sides gives us the equation |y|= 8 so y could be 8 or -8

your book is wrong or you gave me the wrong equation.

Solving the second equation for |m| by subtracting 1 from both sides gives us |m| = -8 this has no solutions because the absolute value is always positive by definition.

Answer 3

Think of absolute value as the distance that a number is from 0 on a number line, this distance is always positive

|y|-6=2

it should be |y| - 6 = - 2

my book says the solution is y=4 or y=-4

how is it both??

since absolute value always yields a positive number, a positive number remains positive and a negative number becomes positive

so |y| - 6 = - 2 can be express as two equations when absolute value is removed

     y = -2+6     and y = - (-2 +6)

  

another problem says |m|+1=-7.

solution: |m|= -8

cannot be a negative number

I don't know what kind of text book you are using but author and publisher along with all of their respective immediate family should all be drawn and quartered.

why isn't it |m|=8 or |m|=-8 like the other one?

how do you know when it's both or one?

Answer 4

You are confusing the solution with the algebraic equation. When an absolute value of a variable is equal to a positive constant, like in the first example (which by the way should be 8 and -8), there are going to be two solutions.

On the other hand, if the absolute value of the variable is equal to a negative constant, there is no solution. The absolute value cannot be negative.

The only other possibility is if it's equal to zero in which case it will have only one solution...zero.

Answer 5

Because |4| = |-4|

Take 1 from both sides ...

Answer 6

If you copied these problems down correctly, then your book is a piece of c**p.

|y| - 6 = 2

|y| = 8

y = 8 or y = -8

|m| = -8 can not be right.  m can be negative ==> m= -8 but absolute value must be positive ==> |m| = 8.