Algebra ( Periods 1 & 4)

Solving Inequalities ( All 4 Op's) 5-1& 5-2

Solving Inequalities 5-2

Again you will use your equation skills but this time use the Multiplicative Inverse Property as you would if you were balancing an equation.

ONE MAJOR DIFFERENCE FROM EQUATIONS:

When you multiply or divide by a NEGATIVE coefficient (to balance) you must SWITCH the inequality SYMBOL (this does NOT apply to adding or subtracting negatives) You must rewrite the problem as you divide by a negative as shown below:

If you want to understand why:    3 < 10      you know that is true

Now multiply both sides by -1 ( multiplication property of equality lets you do that)
but you get -3 < -10 but THAT IS NOT TRUE

You have to SWITCH THE SYMBOL to make it true  -3 > -10

REMEMBER: When you MULTIPLY or DIVIDE by a NEGATIVE, the symbol SWITCHES!

Doing 2 Steps with Inequality Signs:  same as equations except make sure you switch the symbols if you multiply or divide by a negative. (Rewrite that portion of the problem—as you multiply or divide)  Always finish with the variable on the left!

Check with whatever solution is the easiest in the solution set. If 0 fits—use it! 

NEVER USE THE BOUNDARY NUMBER   for instance if your solution was x ≤  4  You could check with any number less than 4—BUT NEVER USE 4!

With two steps—before you start, you may want to clear fractions or decimals but if you don’t mind using them—just get started with the checklist below: If you want to clear them- you should do that right after you distribute ( which is between Steps 1 and 2 below)

1     1, Do Distributive Property first (if necessary) do it carefully

2      2.  Combine like terms on each side of the “WALL”

3   3.  “JUMP” the variables to one side of the wall—that is get all the variables on one side of the inequality by using the Additive Inverse Property (add or subtract using the opposite sign of the variable term

4     4.   Add or subtract

5      5.  Multiple or divide ( only FLIP THE SYMBOL if you multiply or divide by a NEGATIVE to balance)

     6.   Make sure the variable is on the LEFT side when finished.

Set builder notation

Get familiar with the following notation

{x│ x≥ 5} is read “ x SUCH THAT c is greater than or equal to 5”

Checking your solutions is an important set. Many students skip this step! Checking the solutions is especially important with inequalities because the direction of the inequality sign is often changed when writing solutions in set builder notation.