What similarities and differences did you notice between the three types of compound inequalities?

Similarities

Adding or subtracting a number from both sides.

Multiplying or dividing both sides by a positive number.

Applying an increasing function to both sides.

Simplifying one or both sides.

Differences

Multiplying or dividing both sides by a negative number changes the direction of an inequality. So we cannot multiply or divide both sides by a variable unless we know that the variable is either always positive or always negative. This is not a concern when solving equalities.

When applying a decreasing function to both sides of an inequality, the direction of the inequality changes.

Swapping both sides of an inequality also changes the direction of an inequality. Again we don't have to worry about this with equalities.

Double inequalities are similar to and compound inequalities, in that their solutions need to satisfy two inequalities. However, solutions to or compound inequalities can include values that are included in either one of the two solution regions.

Step-by-step explanation:

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step-by-step explanation:

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