 # Solve two-step equations. 3.4 Objective The student will be able to:

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solve two-step equations. 3.4 Objective The student will be able to:

To solve two-step equations, undo the operations by working backwards. Ask yourself: 1.What is the first thing we are doing to x? 2.What is the second thing? To undo these steps, do the opposite operations in opposite order.

1.Draw “the river” 2.Add 3 to both sides 3.Simplify 4.Clear the fraction - Multiply both sides by 2 5.Simplify 6.Check your answer Example 1: Solve this two step equation + 3 + 3 = - 4 x = -8 -4 – 3 = -7 2 · · 2

2) Solve 2x - 1 = -3 + 1 + 1 2x = -2 2 2 x = -1 2(-1) - 1 = -3 -2 – 1 = -3 1.Draw “the river” 2.Add 1 to both sides 3.Simplify 4.Divide both sides by 2 5.Simplify 6.Check your answer

+ 4 + 4 3 · · 3 x = 36 12 – 4 = 8 3) Solve 1.Draw “the river” 2.Add 4 to both sides 3.Simplify 4.Clear the fraction - Multiply both sides by 3 5.Simplify 6.Check your answer

4) Solve 3y – 1 = 8 1.y = 3 2.y = -3 3.y = 4.y = Answer Now

5) Solve d – 4 = 6 + 4 + 4 d = 10 1.Draw “the river” 2.Clear the fraction - Multiply both sides by 2 3.Simplify 4.Add 4 to both sides 5.Simplify 6.Check your answer

6) Solve 1.d = -7 2.d = -19 3.d = -17 4.d = 17 Answer Now

7) Solve -3 -3 a = 35 1.Draw “the river” 2.Subtract 3 from both sides 3.Simplify 4.Clear the fraction – Multiply both sides by -7 5.Simplify 6.Check your answer

8) Solve 5z + 16 = 51 1.z = -35 2.z = -7 3.z = 35 4.z = 7 Answer Now

- 1 - 1 5 · · 5 3x = 15 3 3 x = 5 9) Solve 1.Draw “the river” 2.Subtract 1 from both sides 3.Simplify 4.Clear the fraction - Multiply both sides by 5 5.Simplify 6.Divide both sides by 3 7.Simplify 8.Check your answer

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