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Algebraic Expressions and Solving Equations: Addition and Subtraction Principles

This lesson focuses on writing verbal phrases as algebraic expressions and understanding the properties of addition and subtraction for solving equations. Students will learn how to express phrases like "a number divided by -13" and "your age seven years from now" in algebraic form. The course emphasizes the Addition and Subtraction Properties of Equality to isolate variables, ensuring students can solve equations effectively. Through guided practice and examples, students will strengthen their problem-solving skills and prepare for upcoming assessments.

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Algebraic Expressions and Solving Equations: Addition and Subtraction Principles

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  1. Math 1-8: Warm-up Write each verbal phrase as an algebraic expression. • $4.75 tax added to the total • a number divided by -13 3. 5 years younger than Kayli 4. half of Jon’s money • If x is your age, write an expression for your age seven years from now.

  2. Math 1-8: Solving Addition and Subtraction Equations Objective: How to solve equations using the Subtraction and Addition Properties of Equality.

  3. Vocabulary • solve – find the value of the variable that makes an equation true • solution – the value for the variable that makes an equation true • inverse operations – pairs of operations that “undo” each other • addition and subtraction • multiplication and division

  4. Properties • Addition Property of Equality • if you add the same number to each side of an equation, the two sides remain equal. 7 = 7 7 + 3 = 7 + 3 10 = 10 • Subtraction Property of Equality • if you subtract the same number from each side of an equation, the two sides remain equal. 5 = 5 5 – 2 = 5 – 2 3 = 3

  5. Golden Rule: What you do to one side… you must do to the other!

  6. Remember… • …your goal is to get the variable by itself on one side of the equal sign • isolating the variable • …to look at the side of the equation with a variable first and “undo” that operation • inverse operation • …you can solve vertically or horizontally

  7. Examples Solve w + 19 = 45. Check your solution. w + 19 = 45 write the equation w + 19 – 19 = 45 – 19 subtract 19 from each side w = 26 19-19=0 and 45-19=26, w is by itself Check: w + 19 = 45 write the equation 26 + 19 ? 45 replace w with 26 –> is it true? 45 = 45 26+19=45

  8. Examples Solve h – 25 = -76. Check your solution. h – 25 = -76 write the equation h – 25 + 25 = -76 + 25 add 25 to each sides h = -51 -25+25=0 and -76+25=-51, h is by itself Check: h – 25 = -76 write the equation -51 – 25 ? -76 replace h with -51 -> is it true? -76 = -76 -51-25=-76

  9. Practice • x – 4 = 12 • 55 = 39 + k 3. v – 10 = -34 4. 13 + x = -29

  10. Assignment • Pg. 48 (14-34e; 30ec) • QUIZ ON 9/4: Lessons 6-9

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