May 23, 2024 · Is this approach correct, or is there a more efficient method to solve these types of equations? Additionally, I would appreciate any resources or references on solving systems of …

@J. Mangaldan: The plot is also a good way to verify the answers. There are something like 24 signed-number operations involved in my algebraic solution below, so even with 99% accuracy per …

May 8, 2017 · However once each possible equation is solved one must put the solution (s) back into the original absolute value equation and calculate the sides to see if equal.

Here since you have two expressions inside absolute value signs you will have two such points. Divide the real line at these points and solve the resulting equations subject to the inequality which arises …

Mar 10, 2016 · With a double absolute value inequality you can usualy just square both sides, remove the absolute value symbol, and then solve the resulting equation.

Jun 1, 2025 · I am currently working on solving equations and inequalities involving absolute values. My current strategy is as follows: Consider the equation: $$\\lvert x-1 \\rvert \\; \\lvert x+2 \\rvert = 3$$ Firs...

It’s entirely possible to solve this system by an exhaustive analysis of cases along the lines on which you’ve begun, but there’s an easier way. Notice that both equations have a term $|x-1|$.

Nov 5, 2015 · When solving an equation with absolute value on both sides, such as $$|2x-1|=|4x+3|$$ how to choose one side of which to use the definition of absolute value? For example, if we apply …

Jul 12, 2019 · How to solve equations with absolute value on both sides? Ask Question Asked 6 years, 5 months ago Modified 6 years, 5 months ago

Aug 14, 2014 · -2 I just solve the equalities without absolute values: LHS = RHS and LHS = -RHS. Then I use a number line test to check values in each interval to determine the intervals of the solution set. …