# Inequalities

Given the numbers \(-2\) and \(3\) marked on the number line below.

The relation between these numbers is shown as \(-2<3\)

Perform the following calculations to determine the nature of the inequality.

Operation | Write the statement | Show the new relation |

Add \(2\) to each | \(-2 + 2 < 3 + 2\) | \(0<5\) |

Subtract \(4\) from each | ||

Add \(– 2\) to each | ||

Subtract \(– 4\) from each | ||

Multiply each by \(3\) | ||

Multiply each by \(-1\) | ||

Divide each by \(2\) | ||

Divide each by \(-1\) |

- As you add or subtract, how does the inequality change?
- As you multiply or divide, how does the inequality change?
- Make a conjecture regarding the nature of the inequality when you add, subtract, multiple, or divide.