Question

Please send the notes of inequalities chapter

Answer 1

Answer:

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Step-by-step explanation:

Two algebraic expressions or real numbers related by the symbol ‘>’, ‘<’, ‘≥’, or ‘≤’ forms an inequality. Statements such as 4x + 2y ≤ 20, 9x + 2y ≤ 720, 9x + 8y ≤ 70 are inequalities. 4 < 6; 8 > 6 are the examples of numerical inequalities. x < 6; y > 3; x ≥ 4, y ≤ 5 are examples of literal inequalities. 4 < 6 < 8, 4 < x < 6 and 3 < y < 5 are examples of double inequalities.

Rules for solving linear equations

Rule 1: The same number can be subtracted or added from both the sides (LHS and RHS) of an equation.

Rule 2: Both LHS and RHS of an equation can be divided or multiplied by the same non-zero number.

For solving the inequalities we follow the same rules except with a difference that the sign of inequality is reversed (< to > and ≤ to ≥) whenever an inequality is divided or multiplied by a -ve number. Some examples of inequalities are:

Strict inequalities: ax + b < 0, ax + b > 0, ax + by < c, ax2+bx+c>0

inequalities: ax + b ≤ 0, ax + b ≥ 0, ax + by ≤ c, ax + by ≥ c, ax2+bx+c≤0

Linear inequalities in one variable: ax + b < 0 ax + b > 0, ax + b ≤ 0 ax + b ≥ 0 [when a ≠ 0]

Linear inequalities in two variable: ax + by < c, ax + by > c, ax + by ≤ c, ax + by ≥ c

Rules for solving an Inequality

We can add or subtract the same number to LHS and RHS of inequality without changing the sign of that inequality.

We can divide or multiply both sides of an inequality by the same positive number.

The sign of the inequality is reversed when both sides (LHS and RHS) are divided or multiplied by the same negative number.