Solve the following linear inequations and graph the solution set on a real number line.
$3 (5 x + 3) \geq 2 (9 x - 17), x \in W$

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Solution

Find the solution for $x$

$3 (5 x + 3) \geq 2 (9 x - 17), x \in W$

$15 x + 9 \geq 18 x - 34$

By taking the like terms to one side of equation, we get,

$18 x - 15 x \leq 34 + 9$

$3 x \leq 43$

$x \leq \frac{43}{3}$

As per the condition given in the question, $x \in W$

Therefore,solution set $x \leq \frac{43}{3}$ is
$x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}$

It can be represented in number line as,

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