## anonymous one year ago Solve for x: |x| − 8 = −5 Can someone explain the steps for how to solve this please?

1. anonymous

the answer is 3, but if you subtract 8-5 that equals 3 which will give you the answer

2. anonymous

its x - 8 = -5 the five is negative tho so..

3. anonymous

I just want to know the steps to figuring this out cuz i know thats not the right answer sorry..

4. mathstudent55

First, add 8 to both sides. Can you do that?

5. LynFran

$|x|-8=-5$ok 1st step it to add 8 to both sides of the equation

6. mathstudent55

$$\large |x| - 8 = -~5$$ $$\large ~~~~~+8~~~~~+8$$

7. anonymous

so 16 and 3?

8. mathstudent55

No. -8 + 8 = 0 -5 + 8 = 3. That is good.

9. mathstudent55

You end up with $$\large |x| = 3$$ Ok so far?

10. anonymous

the 8 is not negative tho its x minus 8 equals negative 5

11. LynFran

example solve for x... $|x|-7=9$$|x|=9+7$$|x|=16$$x=\pm 16$

12. mathstudent55

In our original equation, -8 (minus eight) means subtract 8. A subtraction can always be written as the sum of the opposite. So -8 means plus the opposite of 8. $$\large |x| - 8 = -5$$ $$\large |x| + (-~8) = -5$$ $$\large~~~~~~~~~~+8~~~~~+8$$ After adding 8 to both sides, you get: $$\large |x| = 3$$

13. mathstudent55

Do you understand now how we add 8 to both sides to isolate $$|x|$$?

14. anonymous

yea

15. anonymous

the options for it tho aren't just one number its one of these x = −13 and x = −3 x = 3 and x = −3 x = 3 and x = 13 No solution

16. anonymous

plus i dont understand how you turned minus eight into negative eight, i dont understand why you would do that cri

17. mathstudent55

Ok. Now we have a simple absolute value equation. On the left side we have just $$|x|$$. This equals a number, 3, on the right side. Whenever you have an absolute value equation where something in absolute value signs equals a number, you separate it into two simple equations, both without absolute signs. This is the pattern. Then I'll show you with your equation. To solve the absolute value equation $$\large |x| = k$$, where k is a non-zero number, solve these two equations $$\large x = k$$ or $$\large x = -k$$

18. LynFran

heres another example ... |dw:1439778127102:dw|

19. mathstudent55

With your problem, the equation now is $$\large |x| = 3$$ We separate it into two equations: $$\large x = 3$$ or $$\large x = -3$$ Since these two equations are already solved for x, that is the final solution.

20. LynFran

yep ^^

21. mathstudent55

Let's go back to the -8 part above that is still bothering you. Subtraction is defined as adding the opposite. 8 - 2 means 8 + (-2) -3 - 4 means -3 + (-4) 5 - (-7) means 5 + 7 In general, for numbers a and b, a - b means a + (-b) That is simply the definition of subtraction. In our equation, we are subtracting 8 from the absolute value of x. We can turn the subtraction of 8 into the addition of the opposite of 8. The opposite of 8 is -8, so $$\large |x| - 8 = |x| + (-8)$$ Then when we add 8 to both sides to eliminate the -8 on the left side, we end up with -8 + 8 which zero. That is how we eliminate the -8 from the left side and end up with only $$\large |x|$$ on the left side.