Question

solve the inequalities and show the graph of the solution in each case on number line

Answer 1

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Answer 2

Answer:

Our solution is

$x\geq\frac{-38}{7}$

Step-by-step explanation:

Given that

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

Lets simplify by taking LCM

$\frac{x}{2}\geq\frac{5(5x - 2)-3(7x-3)}{15}$

$\frac{x}{2}\geq\frac{25x - 10 - 21x - 9}{15}$

$\frac{x}{2}\geq\frac{4x - 19}{15}$

Multiplying both sides of inequality by 30

$30\frac{x}{2}\geq30\frac{4x - 19}{15}$

$15x\geq8x - 38$

rearrnging

$15x - 8x\geq - 38$

$7x\geq - 38$

$x \geq\frac{-38}{7}$

So our solution is $x\geq\frac{-38}{7}$

The graph on numbered line is given below