Why do we end up with two solutions for equations involving absolute value?

You can think of the absolute value of any number as representing how far it is from zero on the number line. Consider |3| and |–3| below. So this is why we end up with two different equations. In the case of only one solution, you end up with an absolute value expression equal to zero.

Why do absolute value equations have solutions?

Because two numbers have the same absolute value (except 0 ). (The solutions are 73 and −1 .)

How do you solve ODE with absolute value?

SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

1. Step 1: Isolate the absolute value expression.
2. Step2: Set the quantity inside the absolute value notation equal to + and – the quantity on the other side of the equation.
3. Step 3: Solve for the unknown in both equations.
4. Step 4: Check your answer analytically or graphically.

What does Y mean in differential equation?

dependent variable
Differential Equation Definition A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable.

Why do we say that an absolute value number Cannot be negative?

Since the absolute value of any number other than zero is positive, it is not permissible to set an absolute value expression equal to a negative number. So, if your absolute value expression is set equal to a negative number, then you will have no solution.

What happens if an absolute value is negative?

The absolute value of a number is its distance away from zero. That number will always be positive, as you cannot be negative two feet away from something. So any absolute value equation set equal to a negative number is no solution, regardless of what that number is.

Why would an absolute value equation have no solution?

Would it be possible for an absolute value equation to have no solutions when?

Why can we separate variables in differential equations?

In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.

When can you drop an absolute value?

So, summarizing we can see that if b is zero then we can just drop the absolute value bars and solve the equation. Likewise, if b is negative then there will be no solution to the equation.