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MJA Ch 7.2 – Solving Equations with Grouping Symbols

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Bellwork Write the equation & solve 1. 5x + 12 = 2x 2. 1.7 + a = 2.5a – 4.9 3. 7x + 3 = 2x + 23 4.4 4 - 4 Solution

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Assignment Review Text p. 332 # 10 - 27

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Before we begin… Please take out your notebook and get ready to work… Yesterday we worked with solving equations with variables on both sides of the equation… In today’s lesson we will look at how to solve equations using grouping symbols…

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Objective 7.2 Student will solve equations that have grouping symbols Students will solve equations with no solutions or an infinite number of solutions

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Quick Review Grouping Symbols Parenthesis ( ) are grouping symbols Brackets { } are grouping symbols Fraction Bars are grouping symbols According to the order of operations when solving equations work with the grouping symbols first If you have multiple grouping symbols work with the inside grouping symbols first…That is if you have parenthesis nested within brackets you do the parenthesis first

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Quick Review Distributive Property – earlier this year we discussed the distributive property which may look like this: 3(x + 5) Generally, what this is saying is to multiply the 3 by everything within the brackets. When you see a number like 3 next to a bracket with no operation sign, then it means to multiply You are required to be able to recognize and know how to work with the distributive property!

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Distributive Property Review 3 (x + 5) 3x Make sure that you multiply what on the outside of the parenthesis with EVERYTHING on the inside of the parenthesis + 15

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Simplest Form An algebraic equation is in its simplest form when there are no like terms and no grouping symbols

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Example 5(a – 4) = 3(a + 1.5) 5a – 20 = 3a + 4.5 + 20 = + 20 5a = 3a + 24.5 -3a = -3a 2a = 24.5 2 = 2 a = 12.25 Write the equation Distributive Property Add 20 to both sides Simplify Subtract 3a from both sides Divide by 2 Solution

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Your Turn In the notes section of your notebook write and solve the equations 1. 3h = 5(h – 2) 2. 6(b – 2) = 3(b + 8.5)

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No Solution Some equations have no solutions. That is no value of the variable will result in a true statement. The solution set is called the null or empty set and is designated with the following symbols: ø or { } Let’s look at an example…

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Example 3x + 2 = 3x - 1 -3x = -3x + 2 = - 1 + 2 ≠ - 1 Solution: ø Write the equation Subtract 3x from both sides Result is not a true statement The solution is a null set

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Infinite Solutions Some equations have all numbers as their solution set. An equation that is true for every value of the variable is called an identity Let’s look at an example….

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Example 2(2x – 1) + 6 = 4x + 4 4x – 2 + 6 = 4x + 4 4x + 4 = 4x + 4 - 4 = -4 4x = 4x 4 = 4 x = x The equation x = x is always true. The solution set is the set of all numbers Write the equation Distributive Property Simplify Subtract 4 from both sides Divide both sides by 4

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Summary In the notes section of your notebook summarize the key concepts covered in today’s lesson Today we discussed: Solving equations with grouping symbols Null & empty sets Identity

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Assignment Text p. 337 # 20 – 33 Reminder: This assignment is due tomorrow I do not accept late assignments You must show your step by step solution to each of the problems

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