(3x – 2)/5 ≤ (4x – 3)/2
Multiply both the sides by 5 we get,
![\[\begin{array}{*{35}{l}} \left( 3x\text{ }-\text{ }2 \right)/5\text{ }\times \text{ }5\text{ }\le \text{ }\left( 4x\text{ }-\text{ }3 \right)/2\text{ }\times \text{ }5 \\ \left( 3x\text{ }-\text{ }2 \right)\text{ }\le \text{ }5\left( 4x\text{ }-\text{ }3 \right)/2 \\ 3x\text{ }-\text{ }2\text{ }\le \text{ }\left( 20x\text{ }-\text{ }15 \right)/2 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3a2dbfdb1d218221209e7164487d799b_l3.png "Rendered by QuickLaTeX.com")
Multiplying both the sides by 2 we get,
![\[\begin{array}{*{35}{l}} \left( 3x\text{ }-\text{ }2 \right)\text{ }\times \text{ }2\text{ }\le \text{ }\left( 20x\text{ }-\text{ }15 \right)/2\text{ }\times \text{ }2 \\ 6x\text{ }-\text{ }4\text{ }\le \text{ }20x\text{ }-\text{ }15 \\ 20x\text{ }-\text{ }15\text{ }\ge \text{ }6x\text{ }-\text{ }4 \\ 20x\text{ }-\text{ }15\text{ }+\text{ }15\text{ }\ge \text{ }6x\text{ }-\text{ }4\text{ }+\text{ }15 \\ 20x\text{ }\ge \text{ }6x\text{ }+\text{ }11 \\ 20x\text{ }-\text{ }6x\text{ }\ge \text{ }6x\text{ }+\text{ }11\text{ }-\text{ }6x \\ 14x\text{ }\ge \text{ }11 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8464d5e9db4a1f50658fcc7ae638a00c_l3.png "Rendered by QuickLaTeX.com")
Dividing both sides by 14, we get
![\[\begin{array}{*{35}{l}} 14x/14\text{ }\ge \text{ }11/14 \\ x\text{ }\ge \text{ }11/14 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c3799b3084cd6aa77e9bfc09e46ae159_l3.png "Rendered by QuickLaTeX.com")
∴ The solution of the given inequation is [11/14, ∞).
(3x – 2)/5 ≤ (4x – 3)/2
Multiply both the sides by 5 we get,
Multiplying both the sides by 2 we get,
Dividing both sides by 14, we get
∴ The solution of the given inequation is [11/14, ∞).