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.
When absolute value appears on both sides of an equals sign, it means that the equations on either side are equal in magnitude, regardless of their sign. In other words, the absolute value of the expressions on both sides is the same.
This can happen in equations involving absolute value functions, where the solution may have two possible values depending on the sign of the expression inside the absolute value. In order to represent both solutions, the absolute value must appear on both sides of the equals sign.
Yes, if the absolute value expressions on both sides are identical and have a positive sign, then the absolute value can be removed from both sides of the equation. However, if the expressions have different signs, then the equation cannot be solved without the absolute value remaining on both sides.
To solve equations with absolute value on both sides, you must first isolate the absolute value expression on one side of the equation. Then, you can remove the absolute value by considering both the positive and negative solutions. Finally, you can solve for the variable as you would in a regular equation.
Yes, if the absolute value expressions on both sides are exactly the same, then there are infinite solutions to the equation. This is because any value for the variable will make both sides of the equation equal. However, if the expressions are different, then there will only be one or two solutions to the equation.