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Introduction to Algebraic Equations

Introduction to Algebraic Equations. Section 3.1. Definitions. Def: A variable expression is a mathematical phrase that uses numbers, variables , and operation symbols. For example 3 x + 2 ( x is the variable.)

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Introduction to Algebraic Equations

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  1. Introduction to Algebraic Equations Section 3.1

  2. Definitions • Def: A variable expression is a mathematical phrase that uses numbers, variables, and operation symbols. • For example 3x + 2 (x is the variable.) • Def: A term is a group of numbers, or variables, or the product/quotient of numbers and variables (not sum or difference).

  3. On a separate piece of paper… • Write your name, the period, and the date • You will answer various questions throughout the lecture on this paper. • You will turn it in at the end of class.

  4. How many terms are there in the following expressions?(on paper, not notebook) 1. 2. 3. • Note: The number of terms is simply the number of expressions being added and subtracted.

  5. Back to your notebook: • Def: If two expressions are equal to each other, you can write this as an equation. • For example, if x + 3 and 2x – 7 have the same value, then x + 3 = 2x – 7.

  6. Which is which? (On separate paper) • Which of the following are expressions? (exp) • Which of the following are equations? (equ) a) 3x + 5 b) 4 = 1+3 c) 7x + 87y + 32z d) 6x e) 2x = 8 f) 7x + 1 = 9x + 2

  7. Equations always have an equals sign, but expressions do not.

  8. To Solve Algebraic Equations 3 + y = 4 • “y” represents an unknown number. • We can figure out the value of that unknown number.

  9. Solving Equations Algebraically Sometimes we cannot look at a problem and deduce what the variable represents. We use “inverse operations” to peel away the layers of information, and discover the value of our unknown.

  10. Inverse Operations (in notebooks) • The opposite They cancel each other out • Multiplication/Division • Addition/Subtraction • Square/square-root • Positives/negatives

  11. For example: x + 3 = 7 Addition (x + 3), so we do the inverse (opposite) and subtract. x + 3 -3 = 7 -3 (Do to both sides) x = 4 Check: 4 + 3 = 7

  12. Solve the following equations:TheSeparate Paper Please  4. x + 7 = –2 5. – 3 + x = 8 6. 4x = 20 7. = 1

  13. Don't write this. LISTEN! 2x+3=11 • 2 multiplied byx, and 3 added to the x • Opposite of multiplication: division • Opposite of addition: subtraction • So, we will need to divideand subtract to solve for x.

  14. sadmep 2x + 3 = 11 Original Problem 2x + 3 –3 = 11 –3 Subtract 3 2x = 8 One-step left: 2x = 8Divide by 2 • 2 x = 4 Check: 2(4) + 3 = 11

  15. Solve for the variable:In your notebook, solve the following equations. 8) 3y – 9 = 63 9) 5a + 6 = 26 10) 2n – 7 = 25

  16. Homework: pg 111-1121-11 odds, 16-32 evens, 39-49 odds

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