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**Objectives The student will be able to:**

Solve two-step equations Solve equations with variables on both sides Solve equations containing grouping symbols. Adapted from original designed by Skip Tyler, Varina High School

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**+ - ÷ • Solve: 8x + 5 = 61 Step 1 Step 2**

Completely UNDO those steps Working in reverse order using inverse operations! Examine the problem Figure out the order that you would DO to solve if you knew the value of the variable. Use PEMDAS! + - ÷ •

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**Solve: 8x + 5 = 61 – 5 – 5 8x = 56 x = 7 8(7) + 5 = 61 8 56 + 5 = 61**

– 5 – 5 8x = 56 x = 7 8(7) + 5 = 61 = 61 Draw “the river” Subtract 5 from both sides Simplify Divide both sides by 8 Check your answer 8

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**Find the value of z if 7z + 5 = 40**

245 5 9 315 Answer Now

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**Solve: + 9 + 9 = 40 −4 −4 a = −160 40 − 9 = 31 Draw “the river”**

= 40 a = −160 40 − 9 = 31 Draw “the river” Add 9 to both sides Simplify Multiply both sides by -4 Check your answer −4 −4

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**Solve: − 8 − 8 = − 20 4 4 y = −80 −20 + 8 = −12 Draw “the river”**

Subtract 8 from both sides Simplify Multiply both sides by 4 Check your answer − 8 − 8 = − 20 y = −80 − = −12 4 4

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Find the value of z if 30 4 100 1.2 Answer Now

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**Solve: = (4)3 m – 8 = 12 + 8 = + 8 m = 20 12/3 = 4 Draw “the river”**

Multiply both sides by 3 Simplify Add 8 to both sides Check your answer = (4)3 m – 8 = 12 + 8 = + 8 m = 20 12/3 = 4

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Find the value of z if 186 51 39 174 Answer Now

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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. Try to move the one that will keep your variable positive.

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**Solve: 3x + 2 = 4x – 1 - 3x - 3x 2 = x – 1 + 1 + 1 3 = x**

3 = x 3(3) + 2 = 4(3) – 1 9 + 2 = 12 – 1 Draw “the river” Subtract 3x from both sides Simplify Add 1 to both sides Check your answer

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**Solve: 8y – 9 = –3y + 2 + 3y + 3y 11y – 9 = 2 + 9 + 9 11y = 11 11 11**

11y = y = 1 8(1) – 9 = –3(1) + 2 Draw “the river” Add 3y to both sides Simplify Add 9 to both sides Divide both sides by 11 Check your answer

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**What is the value of x if 3 – 4x = 18 + x?**

– 3 3 Answer Now

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**Solve: 4 = 7x – 3x 4 = 4x 4 4 1 = x 4 = 7(1) – 3(1) Draw “the river”**

1 = x 4 = 7(1) – 3(1) Draw “the river” – Notice the variables are on the same side! Combine like terms Divide both sides by 4 Simplify Check your answer

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**Solve: – 7(x – 3) = – 7 – 7x + 21 = – 7 – 21 – 21 – 7x = – 28 – 7 – 7**

– – 21 – 7x = – 28 – – 7 x = 4 – 7(4 – 3) = – 7 – 7(1) = – 7 Draw “the river” Distribute Subtract 21 from both sides Simplify Divide both sides by -7 Check your answer

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**What is the value of x if 3(x + 4) = 2(x – 1)?**

-14 -13 13 14 Answer Now

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**Solve: 3 - 2x = 4x – 6 + 2x +2x 3 = 6x – 6 + 6 + 6 9 = 6x 6 6**

Draw “the river” Clear the fraction – multiply each term by the LCD Simplify Add 2x to both sides Add 6 to both sides Divide both sides by 6 Check your answer 3 - 2x = 4x – 6 + 2x +2x = 6x – 6 = 6x or 1.5 = x

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**– 2x – 2x 5 = – 3 This is never true! No solutions**

Special Case # ) 2x + 5 = 2x – 3 – 2x – 2x 5 = – 3 Draw “the river” Subtract 2x from both sides Simplify This is never true! No solutions

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**Infinite solutions or identity**

Special Case # (x + 1) – 5 = 3x – 2 3x + 3 – 5 = 3x – 2 3x – 2 = 3x – 2 – 3x – 3x – 2 = – 2 Draw “the river” Distribute Combine like terms Subtract 3x from both sides Simplify This is always true! Infinite solutions or identity

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**What is the value of x if – 3 + 12x = 12x – 3?**

4 No solutions Infinite solutions Answer Now

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**Challenge! What is the value of x if – 8(x + 1) + 3(x – 2) = – 3x + 2?**

-8 -2 2 8 Answer Now

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