 # Solving Equations with Variable on Both Sides Objective: Students will solve equations with variables on both sides. Section 3.4.

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Solving Equations with Variable on Both Sides Objective: Students will solve equations with variables on both sides. Section 3.4

Examples to discuss: Don’t have to distribute or combine like terms!!! Solve each equation. Remember get the variable on the same side of the equation!!! 1. 7x + 19 = -2x + 552. 80 – 9y = 6y

Solve the following: First, combine your like terms, then complete the Do/Undo chart

Solve (do the distributive property and then combine like terms before you complete the DO/UNDO chart):

Now, lets solve an equation with variables on both sides Solve. 3x + 2 = 4x - 1 You need to get the variables on one side of the equation. It does not matter which variable you move. But, try to move the one that will keep your variable positive.

Solve 3x + 2 = 4x - 1 - 3x 2 = x - 1 + 1 + 1 3 = x 3(3) + 2 = 4(3) - 1 9 + 2 = 12 - 1 1.Draw a vertical line 2.Subtract 3x from both sides 3.Simplify 4.Add 1 to both sides 5.Simplify 6.Check your answer

More examples to discuss: You have to combine like terms 1st!!! Solve each equation. Remember to combine like terms 1 st !!! 1.3x – 10 + 4x = 5x – 7 2.–x + 6 – 5x = 14 – 2x

1.-3 2. -1/3 3.1/3 4.3 What is the value of x if 3 - 4x = 18 + x? Answer Now

What is the value of x if 3(x + 4) = 2(x - 1)? Answer Now 1.-14 2.-13 3.13 4.14

Special Case #1 2x + 5 = 2x - 3 -2x 5 = -3 This is never true! No solutions 1.Draw a vertical line 2.Subtract 2x from both sides 3.Simplify

Special Case #2 3(x + 1) - 5 = 3x - 2 3x + 3 – 5 = 3x - 2 3x - 2 = 3x – 2 -3x -3x -2 = -2 This is always true! Infinite solutions or identity 1.Draw a vertical line 2.Distribute 3.Combine like terms 4.Subtract 3x from both sides 5.Simplify

What is the value of x if -3 + 12x = 12x - 3? 1.0 2.4 3.No solutions 4.Infinite solutions Answer Now

Challenge! What is the value of x if -8(x + 1) + 3(x - 2) = -3x + 2? Answer Now 1.-8 2.-2 3.2 4.8

Try these examples: 1.15 – 2y = 3y 2.r – 2 + 3r = 6 + 5r 3.34 – 3x = 14x 4.1. 5y – 2 = y + 10 5.6x + 3 = 8 + 7x + 2x

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