Solve the given inequation, and graph the solution on the number line: 2y – 3 < y + 1 ≤ 4y + 7; y ∈ R. - Noon Academy

Solve the given inequation, and graph the solution on the number line: 2y – 3 < y + 1 ≤ 4y + 7; y ∈ R.

Class 10 | Exercise 1 | ICSE | Linear Inequations | Maths | ML Aggarwal

Solve the given inequation, and graph the solution on the number line: 2y – 3 < y + 1 ≤ 4y + 7; y ∈ R.

According to question,

$2y\text{ }\text{ }3\text{ }<\text{ }y\text{ }+\text{ }1\text{ }\le \text{ }4y\text{ }+\text{ }7$

Therefore,

we get

$2y\text{ }\text{ }3\text{ }<\text{ }y\text{ }+\text{ }1$

and

$y\text{ }+\text{ }1\text{ }\le \text{ }4y\text{ }+\text{ }7$

$2y\text{ }\text{ }y\text{ }<\text{ }1\text{ }+\text{ }3$

and

$y\text{ }\text{ }4y\text{ }\le \text{ }7\text{ }\text{ }1$

$y\text{ }<\text{ }4\text{ }and\text{ }-3y\text{ }\le \text{ }6$

$y\text{ }<\text{ }4\text{ }and\text{ }-y\text{ }\le \text{ }2\Rightarrow y\text{ }\ge \text{ }-2$

Hence,

$-2\text{ }\le \text{ }y\text{ }<\text{ }4$

The solution set is:

$~\{y\text{ }:\text{ }-2\text{ }\le \text{ }y\text{ }<\text{ }4,\text{ }y\in R\}$

Representing the solution on a number line:

ML Aggarawal Solutions for Class 10 Chapter 4 - 27

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