{"id":32940,"date":"2024-04-03T07:12:12","date_gmt":"2024-04-03T07:12:12","guid":{"rendered":"https:\/\/moonpreneur.com\/math-corner\/?p=32940"},"modified":"2024-04-03T12:28:16","modified_gmt":"2024-04-03T12:28:16","slug":"what-is-an-inequality-in-math","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/what-is-an-inequality-in-math\/","title":{"rendered":"What is an Inequality in Math"},"content":{"rendered":"\t\t
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In mathematics, equations act as a basis for understanding relationships between quantities. However, not all mathematical relationships can be confined to equality, giving rise to the concept of inequalities, which broadens our understanding by encompassing relationships of greater than, less than, or not equal to.\u00a0<\/span><\/p>

Inequalities play- a significant role in various branches of mathematics, offering insights into comparisons, constraints, and real-world scenarios.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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WHAT IS INEQUALITY?<\/b><\/span><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Inequalities in mathematics express comparisons between quantities, diverging from equations’ balanced relationships. Symbols like <, >, \u2264, or \u2265 denote these inequalities. For instance, if a smartphone costs $450, and the budget is $500, the inequality ‘Cost of smartphone \u2264 Budget’ ensures affordability. Similarly, speed limits, temperature constraints, and age requirements are represented using inequalities. They offer concise ways to express constraints, such as speed \u2264 65 mph, oven temperature \u2264 350\u00b0F, and age \u2265 10 years.\u00a0<\/span><\/p>

Inequalities play a crucial role in various real-world scenarios, facilitating clear comparisons and constraints with efficiency and precision.<\/span><\/p>

Equality and Inequality<\/b><\/h4>

The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, or equal to, or greater than or equal to the other things.<\/span><\/p>

‘p \u2260 q’ signifies that ‘p’ is not equal to ‘q’.<\/span><\/p>

‘p < q’ implies that ‘p’ is less than ‘q’.<\/span><\/p>

‘p > q’ suggests that ‘p’ is more significant than ‘q’.<\/span><\/p>

‘p \u2264 q’ indicates that ‘p’ is less than or equal to ‘q.’<\/span><\/p>

‘p \u2265 q’ denotes that ‘p’ is greater than or equal to ‘q.’<\/span><\/p>

Each symbol represents a distinct relationship.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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RULES OF INEQUALITIES<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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The rules of inequalities are special. Here are the rules of inequality with examples.<\/span><\/p>

Rule 1: Transitive:\u00a0<\/b> <\/span><\/span><\/h4>

If ‘p’ is less than ‘q,’ and ‘q’ is less than ‘d’, then ‘p’ must be less than ‘d’.<\/span><\/p>

Example:<\/span><\/p>

If a<b and b<c, then a<c.<\/span><\/p>

For instance, if 2<5 and 5<8, then 2<8.<\/span><\/p>

Rule 2: Symmetric<\/b>: <\/span><\/span><\/h4>

Swapping ‘p’ and ‘q’ reverses the inequality direction.<\/span><\/p>

Example: If a<b, then b>a.\u00a0<\/span><\/p>

This means that if 3 < 7, then 7>3.<\/span><\/p>

Rule 3: Addition and Subtraction:\u00a0<\/b><\/span><\/h4>

Adding or subtracting the same value from both sides preserves the inequality relationship.<\/span><\/p>

Example:\u00a0<\/span><\/p>

If\u00a0 a<b, then a+c<b+c.\u00a0<\/span><\/p>

For instance, if 2 < 5, then 2 + 3 < 5 + 3, which simplifies to 5 < 8<\/span><\/p>

Rule 4: Multiplication and Division:\u00a0<\/b><\/span><\/h4>

Multiplying or dividing by positive values maintains inequality while multiplying or dividing by negative values necessitates reversing the inequality direction.<\/span><\/p>

Example:\u00a0<\/span><\/p>

If a<b and c>0, then ac<bc.\u00a0<\/span><\/p>

For example, if 2 < 5 and 3 > 0, then 2 \u00d7 3 < 5 \u00d7 3, which simplifies to 6 < 15.<\/span><\/p>

Rule 5: Negation:<\/span>\u00a0<\/b><\/h4>

Introducing negatives inversely affects the inequality direction.<\/span><\/p>

Example:<\/span><\/p>

If a<b, then -a>-b<\/span><\/p>

for instance, if 4<7, then -4>-7<\/span><\/p>

Rule 6: Reciprocal:\u00a0<\/b><\/span><\/h4>

Taking the reciprocal of positive values reverses the inequality direction.<\/span><\/p>

Example:<\/span><\/p>

If a<b and a,b>0, then 1\/a>1\/b<\/span><\/p>

For example, 2<5 and 2,5>0, then 1\/2>1\/5<\/span><\/p>

Rule 7: Square Property:\u00a0<\/b><\/span><\/h4>

Squaring a number yields a result greater than or equal to zero.<\/span><\/p>

Example:<\/span><\/p>

Given a=3, b=-2, and c=0, for a^2, b^2 and c^2:<\/span><\/p>

Then,\u00a0<\/span><\/p>