Inequalities

Question 0

Solving inequalities:
Method 1:
8 - 3x < 7

Answer 0

8 - 3x < 7 (+3x)
8 < 3x + 7 (-7)
1 < 3x (/3)
1/3 < x

Question 1

Representing inequalities on a number line:
x < 2
x < x <= 3

Answer 1

<———o (Coloured in)

• ———-!———–
  - 1

  o---------------o     (Last circle coloured in)

• —-!—————–!———-
  - 2 3

Question 2

Solving inequalities:
Method 2:
8 - 3x < 7

Answer 2

8 - 3x < 7     (-8)
-3x < -1     (/-3)
x > 1/3
   ^
Sign switched because you divided by a negative

Question 3

Graphical inequalities:

What are the three steps?

Answer 3

1. Change inequality into an equation
2. Decide whether line is dotted or full
   — : < or >
   ___ : =
3. Decide which side to shade. This could involve checking a coordinate.