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Equations & inequalities

Learn about equations, the properties of equality, and how to solve them using reflexive, symmetric, transitive, addition, subtraction, multiplication, division, and substitution properties. Discover the laws of exponents and review important concepts.

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Equations & inequalities

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  1. Equations & inequalities Properties

  2. What are equations? • Equations are mathematical sentences that state two expressions are equal. • Example: 2x – 5 = 3(x + 4)

  3. What are the properties of equality? • In order to solve equations in, you must perform operations that maintain equality on both sides of the equation using the properties of equality. • Properties of Equality • Reflexive property of equality • Symmetric property of equality • Transitive property of equality • Addition property of equality • Subtraction property of equality • Multiplication property of equality • Division property of equality • Substitution property of equality

  4. Properties of equality Reflexive Property of Equality Symmetric Property of Equality • a = a • A number is equal to itself. • -5 = -5 • If a = b, then b = a. • If numbers are equal, they will still be equal if the order is changed. • If x = 2, then 2 = x

  5. Properties of equality Transitive Property of Equality Addition Property of Equality • If a = b and b = c, then a = c. • If numbers are equal to the same number, then they are equal to each other. • If a = b, then a + c = b + c. • Adding the same number to both sides of an equation does not change the equality of the equation. • x = 6 x + 2 = 6 + 2

  6. Properties of equality Subtraction Property of Equality Multiplication Property of Equality • If a = b, then a − c = b − c. • Subtracting the same number from both sides of an equation does not change the equality of the equation. • x = 6 x − 2 = 6 − 2 • If a = b and c ≠ 0, then a • c = b • c. • Multiplying both sides of the equation by the same number, other than 0, does not change the equality of the equation. • x = 6 x • 2 = 6 • 2

  7. Properties of equality Division Property of Equality Substitution Property of Equality • If a = b and c ≠ 0, then a ÷ c = b ÷ c. • Dividing both sides of the equation by the same number, other than 0, does not change the equality of the equation. • If x = 6 then • If a = b, then b may be substituted for a in any expression containing a. • If two numbers are equal, then substituting one in for another does not change the equality of the equation.

  8. Properties of operations (Review)

  9. What property?????

  10. What property?????

  11. What about inequalities?

  12. Laws of Exponents/Review • Multiplication of Exponents • Power of Exponents • Division of Exponents • Exponents of Zero • Negative Exponents

  13. Multiplication of Exponents General Rule: Specific Example:

  14. Power of Exponents General Rule: Specific Example:

  15. Division of Exponents General Rule: Specific Example:

  16. Exponents of Zero General Rule: Specific Example:

  17. Negative Exponents General Rule: and Specific Example: and

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