Nelo said:Homework Statement
|2x-8| + |12 - 3x | = 0
Homework Equations
what do i do when it = 0
The Attempt at a Solution
I tried solving it like all the others, but i know there is a unique thing to do when it = 0, i jus don't know what.
So , here's what i did.
2|x-4| + -3|x-4| = 0
-|x-4| = 0
x > 4
(-)x-4 = 0
-x = 4
x = -4
x < 4
(-)-x+4 = 0
x+4 = 0
x = - 4.
The answer is 4, I just probably set the normal one up wrong, what am i doing wrong?
An absolute value equation is an equation that contains an absolute value expression, which is represented by two vertical bars enclosing a value. The absolute value of a number is its distance from 0 on a number line, regardless of its sign. In an equation, the absolute value expression is set equal to a constant or another expression.
To solve an absolute value equation, first isolate the absolute value expression on one side of the equation. Then, write two separate equations without the absolute value symbols: one with the positive value of the expression and one with the negative value. Solve both equations separately and check if the solutions satisfy the original equation.
Solving absolute value equations is useful in finding the possible values of a variable that satisfy a given equation. These equations often represent real-life situations, such as distance, temperature, or time problems, where the solution must be a positive value. Solving absolute value equations can also help in graphing functions and solving inequalities.
Yes, an absolute value equation can have multiple solutions. When solving an absolute value equation, it is essential to check both solutions obtained from the positive and negative expressions to ensure they are valid solutions to the original equation.
Some common mistakes when solving absolute value equations include not isolating the absolute value expression, forgetting to write two separate equations, and not checking the solutions. It is also crucial to remember the properties of absolute value, such as the absolute value of a negative number being positive, and the absolute value of a positive number being itself.