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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

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

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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)

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

$rightwards double arrow$    $3 minus 3 x less than 2 x plus space 8 space rightwards double arrow space minus 3 x minus 2 x space less than space 8 minus 3 space rightwards double arrow negative 5 x less than 5$

$rightwards double arrow$    $fraction numerator negative 5 straight x over denominator negative 5 end fraction greater than fraction numerator 5 over denominator negative 5 end fraction$ (∵ -5 < 0)

$rightwards double arrow$ x > - 1

Hence, the solution of the inequality is $left parenthesis negative 1 comma space infinity right parenthesis$

Graph on the number line is:

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