Linear Inequalities

Solve $24x < 100$, when (i) $x$ is a natural number. (ii) $x$ is an integer.

Solve $-12x > 30$, when (i) $x$ is a natural number. (ii) $x$ is an integer.

Solve $5x - 3 < 7$, when (i) $x$ is an integer. (ii) $x$ is a real number.

Solve $3x + 8 > 2$, when (i) $x$ is an integer. (ii) $x$ is a real number.

Solve the inequality for real $x$: $4x + 3 < 5x + 7$

Solve the inequality for real $x$: $3x - 7 > 5x - 1$

Solve the inequality for real $x$: $3(x - 1) \leq 2(x - 3)$

Solve the inequality for real $x$: $3(2 - x) \geq 2(1 - x)$

Solve the inequality for real $x$: $x + \frac{x}{2} + \frac{x}{3} < 11$

Solve the inequality for real $x$: $\frac{x}{3} > \frac{x}{2} + 1$

Solve the inequality for real $x$: $\frac{3(x - 2)}{5} \leq \frac{5(2 - x)}{3}$

Solve the inequality for real $x$: $\frac{1}{2}\left(\frac{3x}{5} + 4\right) \geq \frac{1}{3}(x - 6)$

Solve the inequality for real $x$: $2(2x + 3) - 10 < 6(x - 2)$

Solve the inequality for real $x$: $37 - (3x + 5) \geq 9x - 8(x - 3)$

Solve the inequality for real $x$: $\frac{x}{4} < \frac{(5x - 2)}{3} - \frac{(7x - 3)}{5}$

Solve the inequality for real $x$: $\frac{(2x - 1)}{3} \geq \frac{(3x - 2)}{4} - \frac{(2 - x)}{5}$

Solve the inequality and show the graph of the solution on number line: $3x - 2 < 2x + 1$

Solve the inequality and show the graph of the solution on number line: $5x - 3 \geq 3x - 5$

Solve the inequality and show the graph of the solution on number line: $3(1 - x) < 2(x + 4)$

Solve the inequality and show the graph of the solution on number line: $\frac{x}{2} \geq \frac{(5x - 2)}{3} - \frac{(7x - 3)}{5}$