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Linear Inequalities

Short Answer Type

1. Solve 24x < 100, when

(i) x is a natural number

(ii) x is an integer

1058 Views

Solve -12x > 30, when

(i) x is a natural number. (ii) x is an integer.

452 Views

Solve 5x – 3 < 7, when

(i) x is an integer. (ii) x is a real number.

474 Views

Solve 3x + 8 > 2, when

(i) x is an integer. (ii) x is a real number.

600 Views

5. Solve the following inequality for real x:

3(x – 1) ≤ 2 (x – 3)

398 Views

6. Solve the following inequality for real x:

3 (2 – x) ≥ 2 (1 – x)

109 Views

7. Solve the following inequality for real x:

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

102 Views

8. Solve the following inequality for real x:

$1 half open parentheses fraction numerator 3 straight x over denominator 5 end fraction plus 4 close parentheses greater or equal than 1 third left parenthesis straight x minus 6 right parenthesis$

space space 1 half open parentheses fraction numerator 3 straight x over denominator 5 end fraction plus 4 close parentheses space greater or equal than space 1 third left parenthesis straight x minus 6 right parenthesis space rightwards double arrow space fraction numerator 3 straight x over denominator 10 end fraction plus 2 greater or equal than straight x over 3 minus 2

Multiply by 30, we have

9 straight x plus 60 greater or equal than 10 straight x minus 60

rightwards double arrow

9 straight x minus 10 straight x greater or equal than negative 60 minus 60 space rightwards double arrow space minus straight x greater or equal than negative 120 space rightwards double arrow space straight x less or equal than 120

(Divide by -1)

rightwards double arrow

straight x element of space left parenthesis negative infinity comma space 120 right square bracket

Hence, the solution set is

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129 Views

9. Solve the following inequality for real x:

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105 Views

10. Solve the following inequality for real x:

fraction numerator left parenthesis 2 straight x minus 1 right parenthesis over denominator 3 end fraction greater or equal than fraction numerator left parenthesis 3 straight x minus 2 right parenthesis over denominator 4 end fraction minus fraction numerator left parenthesis 2 minus straight x right parenthesis over denominator 5 end fraction

127 Views