The given inequality is 2( x #x2212;1 ) #x003C;x+5 (1) 3( x+2 ) #x003E;2 #x2212;x (2) Solve the inequality (i) ...

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Different Types of Intervals in Inequality

8.2x-1 2-x

Question

8.2(x-1) 2-x

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Solution

The given inequality is

2( x−1 )<x+5 (1)

3( x+2 )>2−x (2)

Solve the inequality (i)

2( x−1 )<x+5 2x−2<x+5 2x−x<5+2 x<7

Further simplify the inequality (i)

x<7 (3)

Solve the inequality (2)

3( x+2 )>2−x 3x+6>2−x 3x+x>2−6 4x>−4

Further simplify the inequality (2)

x> −4 4 x>−1 (4)

Consider both (3) and (4) inequalities together.

x<7 and x>−1

The graphical representation of the solution is shown below:

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