Topic/Skill Definition/Tips
Topic: Inequalities Example
1. Inequality An inequality says that two values are not 7≠3
equal.
x≠0
a ≠ b means that a is not equal to b.
2. Inequality x >2 means x is greater than 2 State the integers that satisfy
symbols x <3 means x is less than 3 −2< x ≤ 4.
x ≥ 1 means x is greater than or equal to 1
x ≤ 6 means x is less than or equal to 6 -1, 0, 1, 2, 3, 4
3. Inequalities Inequalities can be shown on a number line.
on a Number x≥0
Line Open circles are used for numbers that are
less than or greater than (¿∨¿)
x <2
Closed circles are used for numbers that
are less than or equal or greater than or
equal (≤∨≥) −5 ≤ x < 4
4. Graphical Inequalities can be represented on a Shade the region that satisfies:
Inequalities coordinate grid. y >2 x , x >1∧ y ≤3
If the inequality is strict ( x >2) then use a
dotted line.
If the inequality is not strict ( x ≤ 6 ) then
use a solid line.
Shade the region which satisfies all the
inequalities.
5. Quadratic Sketch the quadratic graph of the Solve the inequality x 2−x−12<0
Inequalities inequality.
Sketch the quadratic:
If the expression is ¿∨≥ then the answer
will be above the x-axis.
If the expression is ¿∨≤ then the answer
will be below the x-axis.
Look carefully at the inequality symbol in
the question. The required region is below the x-axis,
so the final answer is:
Look carefully if the quadratic is a positive −3< x < 4
or negative parabola.
If the question had been ¿ 0 , the answer
would have been:
x ←3∨x >4
6. Set Notation A set is a collection of things, usually {3 , 6 , 9 } is a set.
numbers, denoted with brackets {}
Mr A. Coleman Glyn School
Topic: Inequalities Example
1. Inequality An inequality says that two values are not 7≠3
equal.
x≠0
a ≠ b means that a is not equal to b.
2. Inequality x >2 means x is greater than 2 State the integers that satisfy
symbols x <3 means x is less than 3 −2< x ≤ 4.
x ≥ 1 means x is greater than or equal to 1
x ≤ 6 means x is less than or equal to 6 -1, 0, 1, 2, 3, 4
3. Inequalities Inequalities can be shown on a number line.
on a Number x≥0
Line Open circles are used for numbers that are
less than or greater than (¿∨¿)
x <2
Closed circles are used for numbers that
are less than or equal or greater than or
equal (≤∨≥) −5 ≤ x < 4
4. Graphical Inequalities can be represented on a Shade the region that satisfies:
Inequalities coordinate grid. y >2 x , x >1∧ y ≤3
If the inequality is strict ( x >2) then use a
dotted line.
If the inequality is not strict ( x ≤ 6 ) then
use a solid line.
Shade the region which satisfies all the
inequalities.
5. Quadratic Sketch the quadratic graph of the Solve the inequality x 2−x−12<0
Inequalities inequality.
Sketch the quadratic:
If the expression is ¿∨≥ then the answer
will be above the x-axis.
If the expression is ¿∨≤ then the answer
will be below the x-axis.
Look carefully at the inequality symbol in
the question. The required region is below the x-axis,
so the final answer is:
Look carefully if the quadratic is a positive −3< x < 4
or negative parabola.
If the question had been ¿ 0 , the answer
would have been:
x ←3∨x >4
6. Set Notation A set is a collection of things, usually {3 , 6 , 9 } is a set.
numbers, denoted with brackets {}
Mr A. Coleman Glyn School
