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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

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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

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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

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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.

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

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17.

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

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

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18.
Solve the following inequality and represent the solution graphically on the number line.

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

5 (2x – 7) – 3 (2x + 3) ≤ 0

$rightwards double arrow$ $10 straight x minus 35 minus 6 straight x minus 9 space less or equal than space 0 space rightwards double arrow space 10 straight x minus 6 straight x less or equal than 9 plus 35 space rightwards double arrow space 4 straight x less or equal than 44 space rightwards double arrow space straight x less or equal than 11$ ...(i)

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

$rightwards double arrow$ $2 straight x minus 6 straight x space less or equal than space 47 minus 19 space rightwards double arrow space minus 4 straight x less or equal than space 28 space rightwards double arrow space fraction numerator negative 4 straight x over denominator negative 4 end fraction greater or equal than fraction numerator 28 over denominator negative 4 end fraction space rightwards double arrow space straight x space greater or equal than space minus 7$ ...(ii)

From (i) and (ii), we have $space space minus 7 less or equal than straight x less or equal than 11$

∴ The solution set is [-7, 11]. Graphically, we have