Sage-Tips

How do you know how many solutions an absolute value equation has?

Has two solutions x = a and x = -a because both numbers are at the distance a from 0. You begin by making it into two separate equations and then solving them separately. An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

How many solutions can a absolute value have?

two solutions
If the absolute value of an expression is set equal to a positive number, expect two solutions for the unknown variable. An absolute value equation may have one solution, two solutions, or no solutions.

How do you know if an absolute value equation has no solution?

Recall that an absolute value expression can never be less than zero. That is, a fully reduced absolute value expression must be greater than or equal to zero. If you’ve simplified an absolute value equation and the value on the other side of the equals sign is a negative number, the equation has no solution.

Why do some absolute value equations have 2 solutions?

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

How many solutions are possible for a regular equation?

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases. One solution. A system of linear equations has one solution when the graphs intersect at a point.

Can an absolute value have 3 solutions?

Yes, it can; for example, |x|=x has the solution set [0,∞) , which contains infinitely many solutions. I hope that this was helpful.

How many solutions are there of an absolute value inequality holds true to all values of real numbers?

The answer to this case is always no solution. The absolute value of any number is either zero (0) or positive. It makes sense that it must always be greater than any negative number. The answer to this case is always all real numbers.

Can absolute value equations have infinitely many solutions?

Yes, it can; for example, |x|=x has the solution set [0,∞) , which contains infinitely many solutions.

Can you think of a situation where there would be one solution for an absolute value?

You can think of the absolute value of any number as representing how far it is from zero on the number line. In the case of only one solution, you end up with an absolute value expression equal to zero. Since this means that the distance from zero on the number line is zero, you end up with only one equation.

Can absolute value have more than 2 solutions?

Absolute value equations are always solved with the same steps: isolate the absolute value term and then write equations based on the definition of the absolute value. There may end up being two solutions, one solution, or no solutions.