Solving inequalities and Interval Notation Workshop
I. Notation
a. Line graph 
b. Set-builder (a, b), [a, b]
c. Interval (x│a ≤ x ≤ b) translated as “x defined as…”
II. Inequalities
a. Less than
b. Greater than
c. Less than or equals to
d. Greater than or equals to
III. Solving inequalities
a. Less than/ greater than
b. Less then or equals to/ greater than or equals to
c. Absolute value (solve separately and linearly )
d. Absolute valueless than 0 (= no sol.)
e. More practice examples
Line graph:
Graph these on a number line .
1. x > 7 
(7, ∞) or {x│x>7}
2. x < 2 
(-∞, 2) or {x│x<2}
3. x ≥ -4 
[4, ∞) or {x│x ≥-4}
4. x ≤ 3 
(-∞, 3] or {x│x≤3}
5. x ≥ 4 and x ≤ 10 
[4, 10] or {x│4≤x≤10}
6. x ≥ -2 and x < 5 [-2, 5) or
{x│-2≤x<5}
7. x ≥ 8 and x ≤ 4 (-∞, 4] U [8, ∞) or {x│x
≤4}or{x│x ≥8}
8. x > 7 and x ≤ 0 
(-∞, 0] U (7, ∞) or {x│x
≤0}or{x│x >7}
Solving Inequalities – just like solving equations except
for – multiplication and -division
When multiplying or dividing by a negative number , flip
the inequality.
What about absolute value?
│-2x + 5│≤ 0 has no solution
Others to try to solve, graph, and put in set-builder
notation and interval notation:
x = all real numbers
x has no solutions
