# Write an absolute value equation that has no solution definition

While this last statement looks more complicated than the beginning statement of 4 - 5x ,it is in a form that can be added, graphed, integrated calculus or differentiated calculus. Sciencing Video Vault 1. At this point we are just trying to develop the skill of writing an absolute value expression without the absolute value symbol. This is worse than what we started with. This is true because as long as x is larger than 4, x - 4 will be positive.

When we encounter such a problem, then either the polynomial is of a special form which allows us to factor it, or we must approximate the solutions with a graphing utility. That costs more than a human haircut at least my haircuts.

Even with the absolute value, we can set each factor to 0, so we get —4 and 1 as critical values. This will give us the following. Welcome to She Loves Math. If they are close to the values above, then you can be pretty sure you have the correct solutions. We are not done, because we need to find values of x that make the original equation true. Check the answers; the work.

At the link you will find the answer as well as any steps that went into finding that answer. We need to treat the absolute value like a variable, and get it out from the denominator by cross multiplying. In certain places, such as calculator and computer programs, you may see it written as abs xwhich naturally means "the absolute value of x," but x is the common way your teacher probably wants you to write it on your homework and tests.

So, since this is the same differential equation as we looked at in Example 1, we already have its general solution. Here are more examples, with explanations. There are no real solutions. However, having found algebraically two numbers that you think are solutions, if the graphing utility shows that intercepts are very close to the numbers you found, then you are probably right.

Note that this piecewise equation is non-continuous. Using the definition of absolute value, there will be only one equation that we will need to set up to get rid of the absolute value, because there is only one place on the number line that is 0 units away from zero: In this case, we have to separate in four cases, just to be sure we cover all the possibilities.

Now that we have isolated the radical term on the right side, we square both sides and solve the resulting equation for x. However, it can be thought of as quadratic in x2. Problem Solution Two students are bouncing-passing a ball between them.

Now we have a product of x and a quadratic polynomial equal to 0, so we have two simpler equations. Try the following few calculations on your calculator: The reasoning here is similar to the last example.

The first equation is trivial to solve. In this case our answer is all real numbers, since an absolute value is always positive. When we do this we will always to try to make it very clear what is going on and try to justify why we did what we did. It might help you to actually substitute z for x2.

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You will also learn how it is used in mathematics. There is no value of x that we can plug in that will be a solution because when we take the absolute value of the left side it will always be positive or zero, NEVER negative.

Answer: No solution. Example 5: Solve the absolute value equation. Therefore, this equation has no solution. In other words, we cannot take the absolute value In other words, we cannot take the absolute value of a number and get a negative.

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Why do you have two solutions when solving absolute value equations? | Yahoo Answers