Science4ver said:Homework Statement
I have an abs-function |x-4|*x -x = 0
which I need to solve.
The Attempt at a Solution
Do I need to re-arrange so I get
|x-4| = x/x = 1
thus we have x-4 = -1 or x-4 = 1.
Hence x = 3 or x = 5 ?
Dick said:You unwisely divided by x. You can only do that if x is nonzero. You are missing a possible value for x.
Science4ver said:well in the assigment x belongs to R.
But how do I obtain the final of x? I am lost here.
mtayab1994 said:And doesn't R contain 0?
Science4ver said:it most certainly does, but what do I do with the equation to obtain the final and third solution?
Dick said:The cleanest way is to factor it into x*(|x-4|-1)=0. How can the product of two numbers be zero?
mtayab1994 said:split x*(l x-4 l -1)=0 into two equations. That should help you even more.
Science4ver said:I know then x is either zero or x is found by solving |x-4|-1 = 0
cool, thanks !
mtayab1994 said:Great ! And what are the values?
Why the question mark? (In both this and your original post.)Science4ver said:x = 0 or x = 3 og x = 5?
HallsofIvy said:Why the question mark? (In both this and your original post.)
What do you get if you put one of those numbers into the original equation?
An absolute value function is a mathematical function that returns the distance of a number from zero on a number line. It can also be thought of as the positive value of a number, regardless of its sign.
To solve an absolute value function, you can follow these steps:1. Set up two equations, one with the positive value inside the absolute value bars and one with the negative value inside.2. Solve each equation separately for the variable.3. Write the two solutions as a compound inequality using "or" to connect the two equations.
Solving an absolute value function algebraically involves using equations and mathematical operations to find the solution, while solving it graphically involves plotting points on a graph and visually identifying the solution.
Yes, an absolute value function can have more than one solution. In fact, it can have an infinite number of solutions depending on the values of the variable and the equation.
To check if a solution to an absolute value function is correct, you can substitute the value into the original equation and see if it satisfies the equation. If the absolute value of the solution is equal to the value inside the absolute value bars, then the solution is correct.