Solving Two- Step Equations Lesson 4-4

Rules to Remember When solving an equation, the goal is to get the variable by itself. 3x + 2 = 9 Addition and Subtraction are opposites Multiplication and Division are opposites

Don’t Forget The equation is like a balance scale. Whatever you do to one side of the equation must be done to the other side of the equation. +5 +5

How to solve two-step equations “Undo” the operations in the reverse order of the order of operations. Work back-words SADMEP Add/Subtract FIRST Multiply/Divide SECOND

Let’s Try One… 3x + 2 = 23 - 2 -2 21 3x = 21 3 3 x = 7 - 2 -2 21 3x = 21 3 3 x = 7 The problem contains addition and multiplication. Which one do we undo 1st?

Another Example -2y – 7 = 3 +7 +7 10 -2y = 10 -2 -2 y = -5 +7 +7 10 -2y = 10 -2 -2 y = -5 The problem contains subtraction and multiplication. Which one do we undo 1st?

Last Example -3c + 9 = 3 -9 -9 -6 -3c = -6 -3 -3 c = 2 -9 -9 -6 -3c = -6 -3 -3 c = 2 The problem contains addition and multiplication. Which one do we undo 1st?

Solving Two-Step Equations Solve each equation. 18 + 3x = 30 18 + 3x = 30 – 18 –18 Subtract 18 from both sides to undo the addition. 3x = 12 3x 3 = 12 Divide both sides by 3 to undo the multiplication. x = 4

Now it’s your turn 5x + 4 = 19 2t + 7 = -1 6m + 1 = -23 -4w – 4 = 8

Solving Two-Step Equations Solve. Check the answer. x 3 – 2 = 1 x 3 – 2 = 1 Add 2 to both sides to undo the subtraction. + 2 +2 x 3 = 3 3 · = 3 · 3 x 3 Multiply both sides by 3. x = 9

Check It Out: Example 1A Solve each equation. 12 + 3x = 27 12 + 3x = 27 – 12 –12 Subtract 12 from both sides to undo the addition. 3x = 15 3x 3 = 15 Divide both sides by 3 to undo the multiplication. x = 5

Check It Out: Example 1B Solve. Check the answer. x 2 – 1 = 2 x 2 – 1 = 2 Add 1 to both sides to undo the subtraction. + 1 +1 x 2 = 3 2 · = 2 · 3 x 2 Multiply both sides by 2. x = 6