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Big Ideas Math Integrated I, 2016 View details

4. Solving Absolute Value Equations

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Exercise 49 Page 33

When does an absolute value equation have no solution?

See solution.

Practice makes perfect

Let's take a look at the given solution. As a first step, the absolute value is removed and the equation is split into two cases.

What we need to do is take a closer look at the given absolute value equation. |2x-1|=- 9 We see that the absolute value expression is isolated on one side and it is set equal to a negative number, - 9. Since absolute value represents a distance, it can never be negative. In other words, there are no values for x that will make the given equation true. It has no solutions.