Absolute value appears on both sides of equals sign

[ECHOSIDE]

Homework Statement

solve for x:

5|7-3x|+2=4|7-3x|-1

Homework Equations

The Attempt at a Solution

7-3x>0
-3x>-7
x<3/7
{x|x<3/7} quantity is positive
{x|x>3/7} quantity is negative

I have never solved an equation with more than one absolute value quantity in it and am not sure how to start. Assistance would be wonderful!

 

[Mark44]

Homework Statement

solve for x:

5|7-3x|+2=4|7-3x|-1

Homework Equations

The Attempt at a Solution

7-3x>0
-3x>-7
x<3/7
{x|x<3/7} quantity is positive
{x|x>3/7} quantity is negative

I have never solved an equation with more than one absolute value quantity in it and am not sure how to start. Assistance would be wonderful!

Simplify your equation first.
1) Add -2 to both sides.
2) Add -4|7-3x| to both sides.

 

[ECHOSIDE]

SOLVED

5|7-3x|+2=4|7-3x|-1
5|7-3x|=4|7-3x|-3
|7-3x|=-3
There are no solutions.

Thanks, Mark44!

 

[mege]

I know you've 'solved' it already - but something that I do for any equation with an 'inner function' is set that inner function to a variable. It makes the equation less daunting to look at (and can be easier/neater to write!).

How much easier does the following look to solve? Set a=|7-3x| and:

5a+2=4a-1

Simplify down, best you can, then put your 'a' back into the equation to finish solving.

 

[QuarkCharmer]

I know you've 'solved' it already - but something that I do for any equation with an 'inner function' is set that inner function to a variable. It makes the equation less daunting to look at (and can be easier/neater to write!).

How much easier does the following look to solve? Set a=|7-3x| and:

5a+2=4a-1

Simplify down, best you can, then put your 'a' back into the equation to finish solving.

That's a great suggestion. I do that with trig functions so I don't get all algebra-ey on them

 

[ECHOSIDE]

Mark44 and mege, thank you for your guidance.
How helpful you both have been! Mege, your suggestion is wonderful. That is a skill I'm adding to my list and will not forget.
This question was my first post on physicsforums.com and I am impressed by and thankful for the responses.
Thank you for involving me in your community.