Conditional Inequality/Examples/Arbitrary Example 1

Examples of Conditional Inequalities

The inequality:

$2 x + 1 > 11$

is a conditional inequality as it is true for $x > 5$ and false otherwise.

Proof

\(\ds 2 x + 1\)

\(>\)

\(\ds 11\)

\(\ds \leadstoandfrom \ \ \)

\(\ds 2 x\)

\(>\)

\(\ds 10\)

\(\ds \leadstoandfrom \ \ \)

\(\ds x\)

\(>\)

\(\ds 5\)

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): inequality
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): inequality: 2.