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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

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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

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)

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16.
Solve the following inequality and show the graph of the solution on the number line.

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

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

Multiply by 30 (the L.C.M. of 2, 3 and 5), we have

15 straight x less than 10 space left parenthesis 5 straight x minus 2 right parenthesis space minus space 6 space left parenthesis 7 straight x minus 3 right parenthesis

rightwards double arrow

15 straight x less than 50 straight x minus 20 minus 42 straight x plus 18 space rightwards double arrow space 15 straight x minus 50 straight x plus 42 straight x less than negative 20 plus 18

rightwards double arrow

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Hence, the solution of the inequality is

open parentheses negative infinity comma space minus 2 over 7 close parentheses

and the graph on the number line is:

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 , $space space 2 straight x plus 19 space less or equal than space 6 straight x plus 47$ .