Why do absolute values have 2 solutions?
And represents the distance between a and 0 on a number line. Has two solutions x = a and x = -a because both numbers are at the distance a from 0. You can write an absolute value inequality as a compound inequality. …
Why are there either two one or no solutions for absolute value equations?
You have seen that absolute value equations have two solutions when the isolated absolute value expression is equal to a positive number. When the absolute value expression is equal to a negative number, there is no solution because absolute value is never negative.
Why can we not get one solution in an absolute value problem?
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.
Do absolute values always have two 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.
When solving an absolute value equation when would you know there is not two solutions?
An absolute value equation has no solution if the absolute value is isolated on one side, but still seems to equal a negative number.
When would an inequality with absolute value have no solution?
Absolute Value Inequalities. Here are the steps to follow when solving absolute value inequalities: Isolate the absolute value expression on the left side of the inequality. If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.
How many solutions does 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.
Can an absolute value inequality have no solution?
The absolute value of any number is either zero (0) or positive which can never be less than or equal to a negative number. The answer to this case is always no solution.