StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q 9.

Expert-verifiedFound in: Page 107

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Write each of the inequalities in interval notation:

$\left|\left({x}^{2}-1\right)+3\right|<0.5$

No solution

An inequality is $\left|\left({x}^{2}-1\right)+3\right|<0.5$

$\begin{array}{rcl}\left|\left({x}^{2}-1\right)+3\right|& <& 0.5\\ -0.5& <& {x}^{2}-1+3<0.5\end{array}$

Here,

${x}^{2}-1+3>0.5$ is true for all width="10" style="max-width: none; vertical-align: -4px;" $x$ and ${x}^{2}-1+3<0.5$ is not true for any value of $x$

So, the given inequality has no solution.

94% of StudySmarter users get better grades.

Sign up for free