Question

solve the absolute value equation |x-3|-5=-3

Answer 1

The really important observation is this:

\(|x-3| = (x-3)\) wherever \(x-3 \ge 0\) or \(x \ge 3\)
\(|x-3| = -(x-3) = (3-x)\) wherever \(x < 3\)

Now you have two simpler problems to work on.

Answer 2

And what is those simpler problems?

Answer 3

You will need to use the substitution principle and the ideas just presented.

Here is your problem statement:
Solve: |x-3|-5=-3

If you PROMISE \(x \ge 3\), this is your new problem statement"
Solve: (x-3)-5=-3

Can you solve this one?

Answer 4

no :/ i don't.

Answer 5

Oh, well then it seems you are in the wrong class or you have been sleeping in class. Let's start from the beginning.

Can you solve this: x - 3 = 2

Answer 6

x=5

Answer 7

Perfect. How about this one?

4x - 12 = 16

Answer 8

x=7

Answer 9

One more:

(x-3)-5=-3

Answer 10

x=5

Answer 11

We are now ready to solve your problem:

If you PROMISE x≥3 , this is your new problem statement:
Solve: (x-3)-5=-3

Can you solve this one?

Answer 12

x=5 right?

Answer 13

Is 5 greater than 3? If so, then you have kept your promise and you have a solution.

Now this one.

If you PROMISE x<3 , this is your new problem statement:
Solve: (3-x)-5=-3

Answer 14

x=1

Answer 15

(3-x) - 5 = -3
Add 5
(3-x) = 2
Add x
3 = 2+x
Subtract 2
1 = x

Good. Is 1 less than 3? If so, you have kept your promise and you have another solution.

Now, go try 5 and 1 in the original problem statement and make sure they work!

Answer 16

thnx i already have my answer