Question

|3+9c| -19 = -1
im supposed to solve and write the solution set.

|3+9c| -19 = -1
i added 19 to both sides
|3+9c|= 18
i subtracted 3 from both sides
9c= 15
i divided both sides by 9 and reduced
so now i have c= 5/3

then i solved for the positive case:
|3+9c| -19 = 1
added 19 on both sides
|3+9c| = 20
subtracted 3 from both sides
9c = 17
divided both sides by 9, so now i have
c= 17/9

so the solution set should be written as: {17/9, 5/3} right?
but the website im doing my work on says this is incorrect and i have no idea what i did wrong?

Answer 1

|3+9c| -19 = -1

Step 1: Add 19 to both sides:

|3+9c| = 18

Step 2: take care of the absolute value sign by separating the equation into two equations separated by the word "or".

3 + 9c = 18 or 3 + 9c = -18

Subtract 3 from both sides:

9c = 15 or 9c = -21

Divide both sides by 9:

c = 15/9 or c = -21/9

Reduce the fractions:

c = 5/3 or c = -7/3

Answer 2

OHHHH oh my god. that makes a lot of sense THANK YOU!

Answer 3

You're welcome.

You can only separate the absolute value equation into two cases (what you called the positive case and the other case you left unnamed) after you have only an absolute value equaling a number.

In your case above, you still had the -19 on the left side when you dealt with the "positive"case. That why your second equation is a different equation from the original equation and gave an incorrect answer.

Answer 4

To solve an absolute value equation of the form

|X| = k,

where X (notice capital X) is an expression in x, and k is a non-negative number,

solve the compound equation:

X = k or X = -k

Notice that you must have only |X| on the left side, just the absolute value of an expression in x (or whatever variable you have).

Answer 5

okay wow that is very helpful-- thank you so much.

I have another problem that's a bit different but i kept doing the same thing i was doing for the previous problem from it.

it's |5x-16| = |9x+15|
i still have to solve and write the solution set, but since it's different i wouldnt use the same method that you showed me to solve the other problem right?

Answer 6

|5x-16| = |9x+15|

Start like we did in the problem before:

5x-16 = |9x+15| or 5x-16 = -|9x+15|

Multiply both sides of the right equation by -1 to isolate the absolute value.

5x-16 = |9x+15| or -(5x-16) = |9x+15|

Now do the same process again (keep in mind the absolute value is the right side):

5x-16 = 9x+15 or -(5x-16) = 9x+15 or -(5x-16) = 9x+15 or 5x-16 = 9x+15

Now we have 4 equations above. Notice that equations 1 and 4 are the same.
Also, equations 2 and 3 are the same.

5x-16 = 9x+15 or -(5x-16) = 9x+15

-4x = 31 or -5x + 16 = 9x + 15

x = -31/4 or -14x = -1

x = -31/4 or x = 1/14

Answer 7

okay, this is a lot clearer now. thank you so much for your help!