Linear Inequalities ISC Class-11 Maths ML Aggarwal Solutions Chapter-7. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe-1, Exe-2, Exe-3, Exe-4, Exe-5 and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

## Linear Inequalities ISC Class-11 Maths ML Aggarwal Solutions Chapter-7

Board | ISC |

Class | 11 |

Subject | Mathematics |

Chapter-7 | Linear Inequalities |

Session | 2024-25 |

Topics | Solutions of ML Aggarwal |

**Linear Inequalities **

**Introduction: ** two variables with its algebraic solution and graphical solution. The linear inequalities are used to solve the problems in different fields like Science, Engineering, Mathematics, and so on.

### Inequalities

Two algebraic expressions or real numbers related by the symbol ≤, ≥, < and > form an inequality. For example: px + qy > 0, 9a – 21b < 0, etc. Equal numbers can be subtracted or added from both the sides of an inequality equation. Also, both sides of an inequality can be divided or multiplied by the same number (non-zero). If both sides of an inequality are divided by the negative number, then the inequality equation gets reversed. The solution of the inequality is the value of x, which makes inequality a true statement.

**Rule 1:** Add or subtract the same number on both the sides of an equation, without affecting the sign of the inequality

**Rule 2:** Multiply or divide both sides of an inequality equation by the same positive number without affecting the sign of the inequality

Now, let us discuss a few examples of solving the linear inequalities in one variable and its graphical representation.

### Graphical Representation of Linear Inequalities in Two Variables

We know that the line divides the cartesian plane into two parts, called the half-plane. The vertical line divides the plane into left and right half-planes, whereas the non-vertical line divides the plane into lower and upper half-planes. The region that contains all the solutions of an inequality is called the solution region. Now, let us solve the inequality graphically

If the inequality involves ‘<’ or ‘>’, we draw the graph of the line as dotted line to indicate that the points on the line are not included from the solution sets.

If the inequality involves ‘≥’ or ‘≤’, we draw the graph of the line as a dark line to indicate the points on the line is included from the solution sets.

Solution of a linear inequality in one variable can be represented on number line as well as in the plane but the solution of a linear inequality in two variables of the type ax + by > c, ax + by ≥ c,ax + by < c or ax + by ≤ c (a ≠ 0, b ≠ 0) can be represented in the plane only.

**Solution of an Inequality**

The value(s) of the variable(s) which makes the inequality a true statement is called its solutions. The set of all solutions of an inequality is called the solution set of the inequality.

**Exe-7.1**

Linear Inequalities ISC Class-11 Maths ML Aggarwal Solutions Chapter-7.

**Exe-7.2**

ISC Class-11 Maths ML Aggarwal Solutions Chapter-7.

**Exe-7.3**

ISC Class-11 Maths ML Aggarwal Solutions Chapter-7.

**Exe-7.4**

Linear Inequalities ISC Class-11 Maths

**Exe-7.5**

Ch-7 Linear Inequalities ISC Class-11 Maths

**Chapter Test**

Linear Inequalities ISC Class-11 Maths Solutions Chapter-7

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