Solveeit Logo
Login

Question

Mathematics Question on Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation

Solve the given inequality and show the graph of the solution on number line: x2≥(5x−2)3−(7x−3)5\frac{x}{2} ≥ \frac{(5x-2)}{3} -\frac{ (7x-3)}{5}.

Answer

x2≥(5x−2)3−(7x−3)5\frac{x}{2} ≥ \frac{(5x-2)}{3} -\frac{ (7x-3)}{5}
⇒x2≥5(5x−2)−3(7x−3)15⇒ \frac{x}{2} ≥\frac{ 5(5x-2) - 3(7x-3)}{15}
⇒x2≥25x−10−21x+915⇒\frac{ x}{2} ≥ \frac{25x-10-21x+9}{15}
⇒x2≥4x−115⇒ \frac{x}{2} ≥ \frac{4x-1}{15}
⇒15x≥2(4x−1)⇒ 15x ≥ 2(4x-1)
⇒15x≥8x−2⇒15x ≥ 8x-2
⇒15x−8x≥8x−2−8x⇒ 15x-8x ≥ 8x-2-8x
⇒7x≥−2⇒ 7x ≥ -2
⇒x≥−27⇒ x ≥ -\frac{2}{7}
The graphical representation of the solutions of the given inequality is as follows.

inequality graph x/2≥5x-2/3-7x-3/5.