Inequalities

Steps to solve Absolute Value Inequalities

1. Isolate the absolute value expression. 2. Create two cases. Use the "KISS" method(keep it, switch, switch) to set up the two cases. 3. Solve both inequalities. 4. Graph your solutions and write your answer in interval notation.

Compound Inequalities

2 or more inequalities graphed on the same line.

Absolute Value Inequalities

Are compound inequalities too!

Rewriting "AND" Inequalities

Because the solutions to an "and" inequality fall between two endpoints, they are frequently written in a more condensed form. Ex. -2<_x<5

Solving Inequalities

Follow the same rules to solve an inequality as you do an equation. Switch the inequality symbol if you multiply or divide by a negative number.

Absolute Value Inequalities (Case 1)

Greater than/ greater than or equal to. Ex. |x|>_7 = x<_-7 & x>_7, Int. Notation: (-&,-7] U [7,&).

Solving "AND" Inequalities

If the "and" inequalitiy is out, solve each part separately. If condensed, you can solve it all together, working inside out. Then, graph to show all possible solutions.

Interval Notation

Is a way to write the solution to an inequality using infinity symbols, parentheses, and brackets. Parentheses indicate "not included" or "open". Brackets indicate "included" or "closed".

Set Notation

Is another way of expressing the solution to an inequality.(ex. x>5, set notation {x|x>5}, read as the set of x values where x is greater then 5.)

Absolute Value Inequalities (Case 2)

Less than/ less than equal to. Ex.|xl<_4 = x>_-4 & x<_4, Int. Notation: [-4,4].

Solving "OR" Inequalities

To solve "or" inequalities, solve each part, then graph on a number line to show the solutions.

Graphing Inequalities

Use a closed dot for _>_/_<_ symbols. Use an open dot for >/< symbols.

"OR"

Written: x _<_-4 or x > 1, Int. Notation: (-&, -4] U (1,&). 《U means or.》

"AND"

Written: x_>_-2 and x<5, Int. Notation: [-2,5).