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**2.4 Solving Equations with Variables on Both Sides**

I can solve equations with variables on both sides and identify equations that are identities or have no solution.

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How to Solve Use properties of equality and inverse operations to produce simpler equivalent equations. Get variables on one side (choose one) Isolate the variable Use inverse operations Check

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**Example 5x + 2 = 2x +14 5x + 2 – 2x = 2x + 14 - 2x 3x +2 = 14**

3𝑥 3 = 12 3 x = 4

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**Using an Equation with Variables on Both sides**

It takes a graphic designer 1.5 h to make one page of a website. With new software, he could complete a page in 1.25 h, but it takes 8 h to learn. How many pages would he have to make in order to save time using the new software? What do we know? What are we looking for? Make an equation 1.5p = 1.25p + 8 p= 32 means with 32 pages the time is the same

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**Solving Using the Distributive Property**

Distribute first, then solve. Examples: 2(5x – 1) = 3(x + 11) 4(2y + 1) = 2(y – 13)

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Identities An equation that is true for every possible value of the variable is an identity. This can happen when variables cancel and you are left with a true statement. Ex: x + 1 = x + 1 After moving variables to one side, you are left with 1 = 1, which is true.

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**Equations with No Solution**

When variables cancel and you are left with a false statement, the equation has no solution. Ex: x + 2 = x – 4 After moving variables to one side, you are left with 2 = -4, which is false.

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**Practice Tell whether the equation is an identity or has no solution.**

10x +12 = 2(5x + 6) 9m – 4 = -3m m 3y – 5 = 3(-2 + y)

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Assignment ODDS ONLY P.105 #11-45

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