To solve two-step equations, undo the operations by working backwards. Recall the order of operations as you answer these questions. Dividing by 2 Subtracting 3 Example: Ask yourself, What is the first thing we are doing to x? What is the second thing? To undo these steps, do the opposite operations in opposite order.

Use a DO-UNDO chart as a shortcut to answering the questions Use a DO-UNDO chart as a shortcut to answering the questions. In the table, write the opposite operations in the opposite order DO UNDO ÷2 -3 Follow the steps in the ‘undo’ column to isolate the variable. Draw “the river” Add 3 to both sides Simplify Clear the fraction -Multiply both sides by 2 Check your answer +3 · 2 + 3 + 3 = - 4 x = -8 -4 – 3 = -7 2 · · 2

1) Solve 2x - 1 = -3 + 1 + 1 2x = -2 2 2 x = -1 2(-1) - 1 = -3 D U 1) Solve 2x - 1 = -3 · 2 - 1 + 1 ÷ 2 + 1 + 1 2x = -2 2 2 x = -1 2(-1) - 1 = -3 -2 – 1 = -3 Draw “the river” Add 1 to both sides Simplify Divide both sides by 2 Check your answer

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

3) Solve 3y – 1 = 8 y = 3 y = -3 y = Answer Now

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

4) Solve d = -7 d = -19 d = -17 d = 17 Answer Now

5) Solve -3 -3 a = 35 D U Draw “the river” Subtract 3 from both sides ÷ -7 + 3 - 3 · -7 Do/Undo Chart – This one is tricky! Remember to always use the sign in front of the number. -3 -3 a = 35 Draw “the river” Subtract 3 from both sides Simplify Clear the fraction – Multiply both sides by -7 Check your answer

6) Solve 5z + 16 = 51 z = -35 z = -7 z = 35 z = 7 Answer Now

7) Solve - 1 - 1 5 · · 5 3x = 15 3 3 x = 5 D U Draw “the river” · 3 ÷ 5 + 1 - 1 · 5 ÷ 3 - 1 - 1 5 · · 5 3x = 15 3 3 x = 5 Draw “the river” Subtract 1 from both sides Simplify Clear the fraction -Multiply both sides by 5 Divide both sides by 3 Check your answer