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Linear Inequations

Define an inequality and understand its classification

• Two real numbers or two algebraic expressions related by the symbols ‘<’, ‘>’, ‘≤’ or ‘≥’ form an inequality.

• For example: 6 < 26, 3 < z + 1 ≤ 22, 27 ≥ s ≥ 16, p + t > 100
• Inequalities can be classified as

• Numerical inequality: Inequalities that involve numbers only are classified as numerical inequalities. For example: 87 < 117, 19 > 17 > 8 etc.
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• Literal inequality: Inequalities that involve a variable on one side and a number on the other side are classified as literal inequalities. For example: a < 6, 18 > k, b ≥ − 27, 21 ≤ m, etc.
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• Double inequality: Inequalities in which the variable or the numbers lie in a certain interval are known as double inequalities. For example: x ∈ [−15, 8], 9 > 6 > 2, 8 ≤ p + 1 ≤ 11, etc.
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• Strict inequality: Inequalities of the type px + q < 0, px + q > 0, px + qy < r, px + qy > r, ax2 + bx + c > 0, or ax2 + bx + c < 0 are classified as strict inequalities. For example: 2x < − 3, x + 17 < 9, x + 3y > 14, 2a + 5b < 8, 2y2 + 5y > 8 etc.
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• Slack inequality: Inequalities of the type px + q ≤ 0, px + q ≥ 0, px + qyr, px + qyr, ax2 + bx + c ≥ 0, or ax2 + bx + c ≤ 0 are classified as slack inequalities. For example: x ≤ 89, 5x + 8y ≤ 9, 8x + y ≥ 7, x + 14 ≥ 28, z2 + 3z ≤ 30 etc.
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• Linear inequality in one variable: Inequalities of the type px + q ≥ 0, px + q ≤ 0, px + q > 0, or px + q < 0, where p ≠ 0, are classified a…

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