SOLVING LINEAR INEQUALITIES
INVESTIGATION – Which mathematical operations preserve an inequality?
Consider the inequality 2 < 4.

ADDITION

2 < 4


SUBTRACTION
2 < 4
MULTIPLICATION
By a +ve number:
By a –ve number:
2 < 4
2 < 4
DIVISION
By a +ve number:
By a –ve number:
2 < 4
2 < 4
When multiplying or dividing an inequality by a negative
number, the inequality sign must be reversed.
linear inequality:
an inequality that contains an algebraic expression of
degree 1 ex. 5x + 3  1
Recall…when graphing inequalities on a real number line:
 or 
use a closed dot 
(inclusion)
 or 
use an open dot 
(exclusion)
Ex 
Solve the following inequality algebraically and graphically.
7+x>2
y
Graph each side of the
inequality as a function and
determine which x-values
are bounded by the lines.
Ex 
x
Solve the following inequality and show a LS/RS check. Represent the solution
on a number line and state the solution in set notation and interval notation.
35 – 3x  21 + x
|
|
–4 –2
|
0
|
2
|
4
Verify:
|
6
|
8
|
10
R
Interval Notation:
square bracket [ or ] indicates inclusion
round bracket ( or ) indicates exclusion
Ex 
Solve the following double inequality. Represent the solution on a number line
and state the solution in set notation and interval notation.
30 < –3(2x + 4) + 2(x + 1) < 46
|
–16
Ex 
|
–14
|
–12
|
–10
|
–8
|
–6
|
–4
| R
–2
Create a linear inequality with both a constant and a linear term on each side
and that has each of the following as a solution:
a)
x<3
b)
Homework:
x  ( –3, 5 ]
p.213–215
#1bd, 2abcf, 3, 5c, 6ace, 7acf, 8 – 11 15, 19