The problem involves solving the equation 5|7-3x|+2=4|7-3x|-1, which features absolute values on both sides. The original poster expresses uncertainty about how to approach solving an equation with multiple absolute value expressions.
The discussion has included various suggestions for approaching the problem, including simplification and substitution strategies. While one participant claims to have solved the equation, others continue to explore different methods and perspectives without reaching a consensus.
The original poster indicates this is their first post on the forum and expresses appreciation for the community's guidance. There is an acknowledgment of the challenge posed by the equation's structure, particularly with multiple absolute values.
ECHOSIDE said: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!
mege said: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.