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# Mathematica Class: Proprietates de Equalitate

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@EasygoingAgate6318

### What is the Addition Property of Equality?

• If a=b, then ac=bc
• If a=b, then a/c=b/c
• If a=b, then a-c=b-c
• If a=b, then a+c=b+c (correct)
• ### What is the Subtraction Property of Equality?

• If a=b, then a+c=b+c
• If a=b, then a-c=b-c (correct)
• If a=b, then a/c=b/c
• If a=b, then ac=bc
• ### What is the Multiplication Property of Equality?

• If a=b, then ac=bc (correct)
• If a=b, then a/c=b/c
• If a=b, then a-c=b-c
• If a=b, then a+c=b+c
• ### What is the Division Property of Equality?

<p>If a=b, then a/c=b/c</p> Signup and view all the answers

### What does the Distribution Property state?

<p>if a(b=c), then a(b=c) = ab+ac</p> Signup and view all the answers

### What does the Substitution Property allow you to do?

<p>Replace a variable with its equal.</p> Signup and view all the answers

### What does the Reflective Property state?

<p>For any real number a, a=a.</p> Signup and view all the answers

### What does the Symmetric Property state?

<p>If a=b, then b=a.</p> Signup and view all the answers

### What does the Transitive Property state?

<p>If a=b and b=c, then a=c.</p> Signup and view all the answers

### Illustrate the idea behind the Substitution Property with an example.

<p>If m+n=15 and n=2, then m+2=15.</p> Signup and view all the answers

### What is an example demonstrating the Division Property of Equality?

<p>If -7k=-42, then k=6.</p> Signup and view all the answers

### Can you provide an example of the Multiplication Property of Equality?

<p>If x/4=-5, x=-20.</p> Signup and view all the answers

### What is a numerical example related to the Addition Property of Equality?

<p>If c-9=-1, then c=8.</p> Signup and view all the answers

### Give an example of the Transitive Property.

<p>If w2=2x and 2x=y, then w2=y.</p> Signup and view all the answers

## Study Notes

### Proprietates de Equalitate

• Subtraction Property of Equality: Si a=b, tunc a-c=b-c. Permitte subtractiones sin afectar la equalitate.
• Multiplication Property of Equality: Si a=b, tunc ac=bc. Valido pro multiplicationes in systemas algebraicos.
• Division Property of Equality: Si a=b, tunc a/c=b/c. Usato quando dividentes sunt identicalmente divided.

### Proprietates Specificas

• Distribution Property: Si a(b=c), tunc a(b+c)=ab+ac. Essential pro expansion de expressiones algebraic.
• Reflexive Property: Omne numero real a satisface a=a. Fundamental pro identitate in mathemathica.
• Symmetric Property: Si a=b, tunc b=a. Permitte reversion de relaciones.
• Transitive Property: Si a=b e b=c, tunc a=c. Usado pro crear relationes indirecte.

### Substitutione e Inversion

• Substitution Property: Si a=b, tunc a pote esser subistituto per b in qualunque expression o equation. Cruciale pro simplificatione de calculationes.
• Reflective Property: Simple affirmation que x=x, affirmando identitate.

### Exemplos de Applicatio

• Example de Distribution: 3(p-7)=3p-21. Demonstration de distributione in action.
• Division Property of Equality: Exemplo: Si -7k=-42, tunc k=6. Clarificatione de division in contextu algebraic.
• Substitution in Operation: Si m+n=15 e n=2, tunc m+2=15. Exemplificando substitutione in operatores.

### Proprietates Repetite e Evoluzioni

• Addition Property Example: Si c-9=-1, tunc c=8. Illustrando additione in actione.
• Symmetric Property Example: Si n=-3, tunc -3=n, logica reversibile in actione.

### Analogias e Comprensiones

• Algebraic Context: Omnes proprietates stabilisce bases solid e logique pro manipulatione de equationes e expressiones algebraicas.
• Fundamentale pro Studentes: Conoscere e applicare iste proprietates es essential pro successu in algebra e geometria.

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## Description

Explora le proprietates fundamental de equalitate in mathematica, inclusa addition, subtraction, multiplication, e division. Understande como isto proprietates supporta le manipulation de expressiones algebraic. Testa tu cognoscentia con questo quiz specific pro le class de mathematica.

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