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**Solving Equations with Variables on Both Sides**

Sol A.4 Chapter Lesson 2-4

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**Step 1 – Use the Distributive Property to remove any grouping symbols**

Step 1 – Use the Distributive Property to remove any grouping symbols. Use properties of equality to clear decimals and fractions. Step 2 – Combine like terms on each side of the equation. Step 3 – Use the properties of equality to get the variable terms on 1 side of the equation and the constants on the other. Step 4 – Use the properties of equality to solve for the variable. Step 5 – Check your solution in the original equation.

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**Solving an Equation w/variables on Both Sides**

5x + 2 = 2x x – 2x + 2 = 2x - 2x x + 2 = 14 3x + 2 – 2 = 14 – 2 3x = 12 (3x)/3 = 12/3 x = 4

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Your turn 7k + 2 = 4k -10

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**Solving an Equation with Grouping Symbols**

2(5x – 1) = 3(x + 11) 10x – 2 = 3x x - 3x - 2 = 3x - 3x x – 2 = 33 7x – = x = 35 (7x)/7 = 35/7 x = 5

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Your turn 4(2y + 1) = 2(y – 13) 7(4 – a) = 3(a – 4)

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An equation that is true for every possible value of the variable is an identity. Example x + 1 = x + 1 An equation that has no solution if there is no value of the variable that makes the equation true. Example x + 1 = x + 2 has no solution.

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**Equations w/Infinitely Many Solutions (Identity)**

10x + 12 = 2(5x + 6) 10x + 12 = 10x + 12 Because 10x + 12 = 10x + 12 is always true, there are infinitely many solutions of the equation. The original equation is an identity.

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**Equation with No Solution**

9m – 4 = -3m m 9m – 4 = -3m + 12m + 5 9m – 4 = 9m + 5 9m - 9m – 4 = 9m - 9m ≠ 5 Because – 4 ≠ 5, the original equation has no solution.

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Your Turn 3(4b – 2) = b 2x + 7 = -1(3 – 2x)

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