7.1.2 Linear Inequalities


7.1.4 Solve Inequalities in One Variable
To solve linear inequalities in one variable, use inverse operation to make the variable as the subject of the inequality.

Example:
Solve the following linear inequalities.
(a) 32x<1 (b)  52x 3 7

Solution:
(a)
 32x<1 32x3<13    2x<2    2x>2    2x 2 > 2 2  x>1

(b)
52x 3 7 ( 52x 3 )×37×3  52x21    2x16    2x16    2x 2 16 2  x8



7.1.5 Simultaneous Linear Inequalities in One Variable
1.   The common values of two simultaneous inequalities are values which satisfy both linear inequalities.
The common values of the simultaneous linear inequalities x ≤ 3 and x > –1 is –1 < x ≤ 3.

2.   To solve two simultaneous linear inequalities is to find a single equivalent inequality which satisfies both inequalities.
 

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