Inequalities
An equation is a statement that uses equals signs to compare two sums. “2+6 = 8†is an equation. Inequalities are statements that use inequality symbols instead of equation signs to compare two sums. “2<6†is an inequality.
There are four inequality symbols: <, >, ≤, and ≥.
They are read as “less than, greater than, less than or equal, greater than or equalâ€.
- Eight is less than fifty: 8<50.
- Fifty is more than eight: 50>8.
- Twice a number is at least eight: 2x≥8.
- Eight is at most twice a number: 8≤2x.
- All positive numbers are greater than zero: x>0.
- All negative numbers are less than zero: x<0.
We use > or < to show which number has a bigger value. This is useful when using variables or stating a property law. We use ≥ or ≤ to get as close to a number without being it. This is useful in calculus limits. We use absolute value bars “| |†to indicate positive numbers. This is useful when numbers must be positive like distance. Distance is always positive. If –4 is 4 units to the left of 0 and 4 is 4 units to the right of 0 then the distance is |±4|.
When dividing or multiplying by a negative you change the sign of the number: 10÷ –2 = –5 and –10 ÷ –2 = 5
When dividing an inequality flip the inequality sign if divisor is a negative number:
(–6 < 10) ÷ –2 = 3 > –5 3 is greater than –5. signs changed we have to “flip†the inequality sign.
(2x ≥ y)/ –2 = x ≤ ½y Plugging in values for x and y will show that flipping the sign is required.