absolute value equations

Question

can someone explain how to solve absolute value equations like this:

x = - |5|^2 - |-2 + 7| x 7

Thanks.

Answer 1

 

Absolute value means that the result of any calculation will be positive.  The difference is shown in the difference between velocity vs. speed.

Velocity is a vector, which means not only does it include the rate of speed, it also includes direction.  Therefore, you can have a negative velocity.  It is not possible to have a negative speed.  Even if you are traveling backwards you are still moving at a postitive speed.

So, to solve the problem you would want to do any of the calculation between the bars first.  Whatever your answer is, you make it positive and then continue the calculation with the modifiers outside of the bars.

e.g.
|5|^2   =25
|-2+7 |=5

so now the problem becomes:
x = -(25) - 5 * 7

In this problem there really is no need for the absolute value markers because what is inside of them is positive anyway.  But if you were to see this for example:

x = -|-5|^2 - |2-7| * 7

...you're answer would still be the same.

 

Answer 2

how do you explain you answer?