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By using a "less than" "greater than" (or combined with equals) they represent a RANGE of answers, not a single discrete value as in an EQUALITY equation...

Basically use the same rules to solve as in a regular algebraic equation (i.e. perform same operation to both sides to keep it balanced)...

NOTE***

The Exception: Negative Numbers. There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

SO... STEP BY STEP:

-4x -9 > 7

*** ADD 9 to each side

-4x > 16

*** DIVIDE each side by 4

-x > 4

*** THIS STEP IS UNIQUE to INEQUALITIES! REVERSE SIGNS OF EACH SIDE, AND REVERSE INEQUALITY!

x < -4

The selected graph (b) shows the correct RANGE of values, i.e. all numbers LESS THAN (but not including) -4!

Make sense?