OTCQ Solve X = -4 3

Aim 3-4/3-5: How do we solve equations by working backwards? How do we reverse PEMDAS? Standards AA6 Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable.

To solve two-step equations, undo the operations by working PEMDAS backwards in most cases. Example: Ask yourself, 1.What is the first thing we are doing to x? 2.What is the second thing? Recall the order of operations as you answer these questions. Dividing by 2 Subtracting 3 To undo these steps, do the opposite operations in opposite PEMDAS 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 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 (PEMDAS) ( Reverse PEMDAS ) ÷2 -3 Follow the steps in the ‘undo’ column to isolate the variable = - 4 x = – 3 = · 2 2 · · 2

1) Solve 2x - 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 x = x = -1 2(-1) - 1 = – 1 = -3 D U · ÷ 2

· · 3 x = – 4 = 8 2) 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 D U ÷ · 3

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

3) Solve Exception to reverse Pemdas approach: If one side is a fraction/ratio then multiply both sides by the denominator first.

3) Solve D U - 4 ÷ 2 · Because everything on the left is divided by 2. So we have to clear the fraction first.

3) Solve d – 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 D U - 4 ÷ 2 · 2 + 4

4) Solve 1.d = -7 2.d = d = d = 17

5) Solve 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 D U ÷ · -7 Do/Undo Chart – This one is tricky! Remember to always use the sign in front of the number.

6) Solve 5z + 16 = 51 1.z = z = -7 3.z = 35 4.z = 7

· · 5 3x = x = 5 7) 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 D U · 3 ÷ · 5 ÷ 3