Solve 5x – 3 < 7, when(i) x is an integer.

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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

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2.

Solve -12x > 30, when

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

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3.
Solve 5x – 3 < 7, when

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

5x – 3 < 7

5x – 3 < 7 $rightwards double arrow$ 5x < 10 $rightwards double arrow$ x<2

∴ (i) When $space space straight x element of space straight Z comma space straight x space equals space 1 comma space 0 comma space minus 1 comma space minus 2 comma space........$
The solution set is $open curly brackets.... comma space minus 3 comma space minus 2 comma space minus 1 comma space 0 comma space 1 close curly brackets$

(ii) When $straight x space element of space straight R comma space space straight x less than 2 space or space straight x space element of space left parenthesis negative infinity comma space 2 right parenthesis$

∴ The solution set is $space space left parenthesis negative infinity comma space 2 right parenthesis$

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4.

Solve 3x + 8 > 2, when

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

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5. Solve the following inequality for real x:

3(x – 1) ≤ 2 (x – 3)

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6. Solve the following inequality for real x:

3 (2 – x) ≥ 2 (1 – x)

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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

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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

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9. Solve the following inequality for real x:

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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

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