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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)

3 (2 – x) ≥ 2 (1 – x)

$rightwards double arrow$ $6 minus 3 straight x greater or equal than 2 minus 2 straight x rightwards double arrow space minus 3 straight x plus 2 straight x greater or equal than 2 minus 6 space rightwards double arrow negative straight x greater or equal than negative 4 rightwards double arrow fraction numerator negative straight x over denominator negative 1 end fraction less or equal than fraction numerator negative 4 over denominator negative 1 end fraction rightwards double arrow straight x less or equal than 4$

(∵ -1 < 0)
$rightwards double arrow$ $straight x space element of space left parenthesis negative infinity comma space 4 right square bracket$

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