1 / 16

The Addition Principle of Equality

2.2. The Addition Principle of Equality. 1. Determine whether a given equation is linear. 2. Solve linear equations in one variable using the addition principle. 3. Solve equations with variables on both sides of the equal sign. 4. Solve identities and contradictions.

euphemia-cathy
Download Presentation

The Addition Principle of Equality

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2.2 The Addition Principle of Equality 1. Determine whether a given equation is linear. 2. Solve linear equations in one variable using the addition principle. 3. Solve equations with variables on both sides of the equal sign. 4. Solve identities and contradictions. 5. Solve application problems.

  2. Addition Principle of Equality Linear equation: An equation in which each variable term contains a single variable raised to an exponent of 1. Linear equation in one variable: An equation that can be written in the form ax + b = c, where a, b, and c are real numbers and a 0. Nonlinear equations:

  3. Addition Principle of Equality 5 5 = 5 5 + 2 5 + 2 = = 5 + 2 Right side Left side We can add (or subtract) the same quantity to (from) both sides of an equation and still have a true statement.

  4. Addition Principle of Equality If a = b, then a + c = b + c for all real numbers a, b, and c. To clear a term in an equation, add the additive inverse of that term to both sides of the equation. Additive Inverse x + 15 is an expression, so we can’t use the addition principle of equality!!!! 5 –5 3 –3 –2x 2x 7x –7x x = 3 is the same as 3 = x.

  5. Addition Principle of Equality Goal: x = some number Additive Inverse: 19 x–19 = –34 Since we added 19 to the left side, we must add 19 to the right side as well. + 19 + 19 x + 0 = –15 x = 15 Check: Replace x with –15 . True, so –15 is the solution.

  6. Addition Principle of Equality Goal: x = some number Additive Inverse: –7 x+ 7 = 20 –7 –7 x + 0 = 13 x = 13 x+ 7 = 20 Check: 13+ 7 = 20 20 = 20 True, so 13 is the solution.

  7. Addition Principle of Equality Goal: m = some number m+ 5 = 12 – 4 Simplify sides if you can. m+ 5 = 8 Additive Inverse: –5 –5 –5 m + 0 = 3 m = 3 Check: m+ 5 = 12 – 4 3 + 5 = 12 – 4 8 = 8 True, so 3 is the solution.

  8. Addition Principle of Equality • To Solve Linear Equations • 1. Simplify both sides of the equation as needed. • a. Distribute to clear parentheses. • b. Combine like terms. • 2. Use the addition principle so that all variable terms are on one side of the equation. • 3. Use the addition principle so that all constants are on the other side.

  9. Addition Principle of Equality Additive Inverse: –2x Solve: –2x–2x Additive Inverse: –5 –5–5 Check:

  10. Addition Principle of Equality Solve: Simplify sides if you can. Additive Inverse: –x –x–x Additive Inverse: –3 –3–3 Check:

  11. Addition Principle of Equality Solve: Simplify sides if you can. Additive Inverse: –x –x–x Additive Inverse: +8 +8+8 Check:

  12. Solve for t. – 8t + 4 +14t = – 4t + 3 + 9t a) t = 5 b) t = 3 c) t = 1 d) t = –1 2.2

  13. Solve for t. – 8t + 4 +14t = – 4t + 3 + 9t a) t = 5 b) t = 3 c) t = 1 d) t = –1 2.2

  14. Addition Principle of Equality Solve: Simplify sides if you can. Additive Inverse: –3x –3x–3x Lost the variable term!! True statement. Identity Solution is ALL REAL NUMBERS. Identity: An equation that has every real number as a solution.

  15. Addition Principle of Equality Solve: Simplify sides if you can. Additive Inverse: –2x –2x–2x Lost the variable term!! False statement. Contradiction There is NO SOLUTION. Contradiction: An equation that has no real number solution

  16. Addition Principle of Equality Solve: Additive Inverse: +3 +3+3 Check:

More Related