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Linear Inequalities

Short Answer Type

11. Solve the following inequality:

6 less or equal than negative 3 left parenthesis 2 straight x minus 4 right parenthesis less than 12

130 Views

12. Solve the following inequality:

negative 3 space less or equal than space 4 minus fraction numerator 7 straight x over denominator 2 end fraction less or equal than 18

135 Views

13. Solve the following inequality:

$space space 7 less or equal than fraction numerator 3 straight x plus 11 over denominator 2 end fraction less or equal than 11$

space space 7 less or equal than fraction numerator 3 straight x plus 11 over denominator 2 end fraction less or equal than 11

Now,

7 less or equal than fraction numerator 3 straight x plus 11 over denominator 2 end fraction rightwards double arrow 14 less or equal than 3 straight x plus 11 space rightwards double arrow space minus 3 straight x less or equal than 11 minus 14

rightwards double arrow

negative 3 straight x space less or equal than space minus 3 space rightwards double arrow space fraction numerator negative 3 straight x over denominator negative 3 end fraction greater or equal than space fraction numerator negative 3 over denominator negative 3 end fraction space rightwards double arrow space straight x space greater or equal than 1

...(i)

Also,

fraction numerator 3 straight x plus 11 over denominator 2 end fraction less or equal than 11 space rightwards double arrow space 3 straight x plus 11 space less or equal than space 22 space rightwards double arrow space 3 straight x space less or equal than space 22 space minus 11 space rightwards double arrow space 3 straight x less or equal than 11 space rightwards double arrow space straight x space less or equal than space 11 over 3

...(ii)

∴ From (i) and (ii), we have

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which is the required solution of the given inequality.

Hence, the solution set is

open square brackets 1 comma space 11 over 3 close square brackets.

125 Views

14. Solve the following inequality:

space space minus 15 less than fraction numerator 3 left parenthesis straight x minus 2 right parenthesis over denominator 5 end fraction less or equal than 0

107 Views

15.

Solve the following inequality and show the graph of the solution on the number line.

3 (1 - x) < 2 (x + 4)

109 Views

16.

Solve the following inequality and show the graph of the solution on the number line.

$straight x over 2 less than fraction numerator left parenthesis 5 straight x minus 2 right parenthesis over denominator 3 end fraction minus fraction numerator left parenthesis 7 straight x minus 3 right parenthesis over denominator 5 end fraction$

390 Views

17.

Solve the following inequality and represent the solution graphically on the number line.

$5 straight x plus 1 greater than negative 24 comma space space space space 5 straight x minus 1 less than 24$

108 Views

18.

Solve the following inequality and represent the solution graphically on the number line.

5 (2x – 7) – 3 (2x + 3) ≤ 0 , $space space 2 straight x plus 19 space less or equal than space 6 straight x plus 47$ .