Chapter 6 : Linear Inequalities

Q. Solve the inequality for real

x

\frac{x}{3} > \frac{x}{2} + 1

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Solve the inequality for real

x

\frac{(2 x - 1)}{3} \geq \frac{(3 x - 2)}{4} - \frac{(2 - x)}{5}

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Q. Solve the inequalities for real

x

3 (x - 1) \leq 2 (x - 3)

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Q. Solve the inequality for real

x

2 (2 x + 3) - 10 < 6 (x - 2)

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Q. Solve the inequality for real

x

\frac{3 (x - 2)}{5} \leq \frac{5 (2 - x)}{3}

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Q. Solve the inequality for real

x

37 - (3 x + 5) \geq 9 x - 8 (x - 3)

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Solve the inequality and show the graph of the solution on number line:

5 x - 3 \geq 3 x - 5

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Solve the inequality and show the graph of the solution on number line:

3 x - 2 < 2 x + 1

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Q. Solve the inequalities for real

x

3 x - 7 > 5 x - 1

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Q. Solve the inequality for real

x

3 (2 - x) \geq 2 (1 - x)

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Q. Solve

5 x - 3 < 7,

when

(i)

x

is an integer.

(ii)

x

is a real number.

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Q. Solve the inequality for real

x

x + \frac{x}{2} + \frac{x}{3} < 11

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Q. Solve

24 x < 100

, when (i)

x

is a natural number. (ii)

x

is an integer

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Q. Solve

- 12 x > 30

, when (i)

x

is a natural number. (ii)

x

is an integer

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Q. Solve

3 x + 8 > 2,

when (i)

x

is an integer. (ii)

x

is a real number

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Q. Solve the inequalities for real

x

4 x + 3 < 5 x + 7

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Q. Solve the inequality for real

x

\frac{1}{2} (\frac{3 x}{5} + 4) \geq \frac{1}{3} (x - 6)

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Solve the inequality and show the graph of the solution on number line:

\frac{x}{2} \geq \frac{(5 x - 2)}{3} - \frac{(7 x - 3)}{5}

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Q. Solve the inequality for real

x

\frac{x}{4} < \frac{(5 x - 2)}{3} - \frac{(7 x - 3)}{5}

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Solve the inequality and show the graph of the solution on number line:

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

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