1. What happens to the direction of an inequality when the same real number is added to both sides?
2. If both sides of an inequality are multiplied by a negative number, what must happen to the inequality sign?
3. Which solution set matches the quadratic inequality x(x-4)>0?
Properties of inequalities — addition?
Inequality remains the same when adding/subtracting the same number.
Properties of inequalities — multiplication?
Same sign: inequality stays; negative sign: inequality reverses.
Reciprocal inequality rule — when?
Reverses only if both sides have same sign.
Squaring inequalities — caution?
Direction may change unless signs are known.
Quadratic inequality — highest power?
Degree 2 polynomial inequality.
Sign analysis — factors?
Determine positivity/negativity by factor signs.
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