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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) 52x37

Solution:
(a)
 32x<132x3<13   2x<2   2x>2  2x2>22 x>1

(b)
52x37(52x3)×37×3 52x21   2x16   2x16  2x2162 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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