Solution and Representation of Inequalities

Solve the following system of inequalities into variables.

$5x+4y\le 40, x\ge 2, y\ge 3$

Graph the solution set $2x-5y\ge -10$

A patient who has undergone a difficult surgery will survive a minimum of $36$ years. Then, his survival time, $x$(in years), can be represented by

If $5x-3\le 5+3x\le 4x+2,$ express it as $a\le x\le b$ and then state the values of $a$ and $b$.

Solution of the system of inequality $x+y\ge 1, 3x+4y<12, x-2y\le 2, x\ge 0, y\ge 0$ has region

The number of non-negative integer solutions of the equations $6x+4y+z=200$ and $x+y+z=100$ is

The solution set of $8x+10\le 18$, $x\in Z$.

The solution set of $3x+9<12$, $x\in R$.

The solution set of $4x-5>7, x\in N$.

$2x-3\ge 3x+5$ can be written as

Write the set of values of $x$ satisfying the inequations $5x+2<3x+8$ and $\frac{x+2}{x-1}<4$.

Write the solution set of the inequation $\left|\frac{1}{x}-2\right|<4$.

Write the set of values of $x$ satisfying $|x-1|\le 3$ and $|x-1|\le 1$.

Write the solution set of the equation $\left|2-x\right|=x-2$.

Solve : $\frac{2x-3}{4}-2\ge \frac{4x}{3}-6, 2\left(2x+3\right)<6\left(x-2\right)+10$.

Solve : $x+5>2\left(x+1\right), 2-x<3\left(x+2\right)$.

Solve ; $4x-1\le 0, 3-4x<0$.

Solve; $11-5x>-4, 4x+13\le -11$.

Solve $3x-1\ge 5, x+2>-1$.

Write the solution of  $2x-3<7, 2x>-4$.