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Chapter 7 Lesson 2 Solving Equations with Grouping Symbols pgs. 334-338

Vocabulary. Null/empty set (336): equations that have no solution. No value of the variable results in a true sentence. Represented by ? or { }Identity (336): an equation that is true for every value of the variable. Josh starts walking at a rate of 2 mph. One hour later, his sister Mari

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Chapter 7 Lesson 2 Solving Equations with Grouping Symbols pgs. 334-338

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    1. Chapter 7 Lesson 2 Solving Equations with Grouping Symbols pgs. 334-338 What you will learn: Solve equations that involve grouping symbols Identify equations that have no solution or an infinite number of solutions

    2. Vocabulary Null/empty set (336): equations that have no solution. No value of the variable results in a true sentence. Represented by ? or { } Identity (336): an equation that is true for every value of the variable

    3. Josh starts walking at a rate of 2 mph. One hour later, his sister Maria starts on the same path on her bike, riding at 10mph What does t represent? Why is Maria’s time shown as t-1? Write an equation that represents the time when Maria catches up to Josh.

    4. Example 1: Solve Equations with Parentheses Solve the equation from the previous chart: 2t = 10(t-1) Write the problem: 2t = 10(t -1)

    5. Now check the previous problem. Josh traveled 2 miles ? 5 hour or 2.5 miles hour 4 Maria traveled 1 hour less than Josh. She traveled: 10 miles ? 1 hour hour 4 or 2.5 miles Therefore, Maria caught up to Josh in 1/4 hour or 15 minutes.

    6. Another Example 1: Solve Equations with Parentheses Solve: 6(n-3) = 4(n + 2.1)

    7. Example 2: Use an Equation to Solve a Problem The perimeter of a rectangle is 20 feet. The width is 4 feet less than the length. Find the dimensions of the rectangle. Then find its area.

    8. Since we know the length is 7 ft, now we need to find the width.

    9. Example 3: No Solution Solve: 12 - h = -h + 3

    10. Example 4: All Numbers as solutions Remember, an equation that is true for every value of the variable is called an identity. Solve: 3(2g + 4) = 6(g+2)

    11. Your Turn! Solve each equation. Check your solution 3(a-5) = 18 3(s+22) = 4(s+12) 4(f+3) + 5 = 17 + 4f 8y - 3 = 5(y - 1) +3y

    12. One More! Find the dimension of the rectangle. P = 460ft

    13. PRACTICE IS BY THE DOOR ON YOUR WAY OUT! QUIZ TOMORROW OVER 7-1 & 7-2

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