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Learn how to solve two-step equations with negative coefficients, combine like terms, and simplify expressions. Practice with step-by-step examples and check your solutions along the way.

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  1. Lesson Menu Main Idea and New Vocabulary Example 1: Solve Two-Step Equations Example 2: Solve Two-Step Equations Example 3: Equations with Negative Coefficients Example 4: Combine Like Terms First

  2. Solve two-step equations. • two-step equation Main Idea/Vocabulary

  3. Solve Two-Step Equations Solve 5y + 1 = 26. Method 1 Use a model. Remove one 1-tile from each mat. Example 1

  4. Solve Two-Step Equations Separate the remaining tiles into 5 equal groups. There are five 1-tiles in each group, so y = 5. Example 1

  5. Solve Two-Step Equations Method 2 Use symbols. Use the Subtraction Property of Equality. 5y + 1 = 26Write the equation. – 1 = – 1 Subtraction Property of Equality 5y = 25 Example 1

  6. Division Property of Equality Solve Two-Step Equations Use the Division Property of Equality. 5y = 25 y = 5 Simplify. Answer: The solution is 5. Example 1

  7. Solve 4b – 3 = 17. A. 3.5 B. 5 C. 14 D. 20 Example 1 CYP

  8. Solve Write the equation. Simplify. 3 • (–6) = 3 • Multiplication Property of Equality Solve Two-Step Equations – 2 = – 2 Subtraction Property of Equality –18 = z Answer: The solution is –18. Example 2

  9. 1 __ Solve h + 12 = 8. 5 A. –20 B. –4 C. 28 D. 100 Example 2 CYP

  10. Division Property of Equality Equations with Negative Coefficients Solve 8 – 3x = 14. 8 – 3x = 14Write the equation. 8 + (–3x) = 14 Rewrite the left side as addition. – 8 = – 8 Subtraction Property of Equality –3x = 6 Simplify. x = –2Simplify. Answer: The solution is –2. Example 3

  11. Write the equation. ? Replace x with –2. ? Multiply. To subtract a negative number, add its opposite. ?  The sentence is true. Equations with Negative Coefficients Check Example 3

  12. Solve 9 = 11 – 2y. A. –10 B. –2 C. –1 D. 1 Example 3 CYP

  13. Division Property of Equality Combine Like Terms First Solve 14 = –k + 3k – 2. Check your solution. 14 = –k + 3k – 2 Write the equation. 14 = –1k+ 3k – 2 Identity Property; k = 1k 14 = 2k – 2 Combine like terms; –1k + 3k = (–1 + 3)k or 2k + 2 = + 2 Addition Property of Equality 16 = 2k Simplify. 8 = k Simplify. Answer: The solution is 8. Example 4

  14. Write the equation. ? Replace k with 8. ? Multiply.  The statement is true. Combine Like Terms First Check Example 4

  15. Solve 4w + 6 – 7w = 15. A. –7 B. –3 C. 3 D. 9 Example 4 CYP

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