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multiply or divide BY a negative number.

When solving inequalities, reverse the inequality symbol when you . . .

Where the two inequalities "overlap"

What is the solution to an "and" compound inequality?

What is the solution to an "or" compound inequality?

Both inequalities "put together" on the same number line

x < 5

x/5 < 25

x < 7

x < 5 or x<7

No Solution

If an inquality is equivalent to an inequality that is false, such as 4 < -2.

5<x<7

x>5 and x<7

x>5 or x<7

all real numbers

positive and negative number

To solve an absolute value equation, drop the absolute value symbol and set what is inside the absolute value equal to a . . .

and

When solving an absolute value INEQUALITY, if the original problem has a less than symbol, what type of compound inequality is it?

or

When solving an absolute value INEQUALITY, if the original problem has a greater than symbol, what type of compound inequality is it?

reverse the inequality symbol

When setting up the "negative" side of the absolute value inequality . . .

3x + 5y >15

dotted; because there is not a line under the greater than sign.

3x + 5y ≤ 15

solid; because there is a line under the less than sign.