Solving Two- Step Equations

Rules to Remember When solving an equation, the goal is to get the variable by itself. Addition and Subtraction are inverse operations. (opposites) Multiplication and Division are inverse operations. (opposites)

Don’t Forget! Whatever you do to one side of the equation…. …. must be done to the other side of the equation.

How to solve two-step equations In order of operations, we do multiplication or division first, then addition and subtraction. 2 x 3 + 6 { 6 + 6 =12 When solving an equation we do the opposite!

3x + 2 = 23 - 2 - 2 3x = 21 3 3 x = 7 Let’s Try One… Addition Multiplication Addition 3x + 2 = 23 - 2 - 2 Reverse order of operations says to undo addition (by subtracting) first… 3x = 21 3 3 Now undo multiplication (by dividing) x = 7

Check! Write original equation….. 3x + 2 = 23 Rewrite original equation with our answer….. 3(7) + 2 = 23 21 + 2 = 23 Do the math….. 23 = 23 

2x + 4 = 14 - 4 - 4 2x = 10 2 2 x = 5 Try Another One… Addition Multiplication Addition 2x + 4 = 14 - 4 - 4 Reverse order of operations says to undo addition (by subtracting) first… 2x = 10 2 2 Now undo multiplication (by dividing) x = 5

Check! Write original equation….. 2x + 4 = 14 Rewrite original equation with our answer….. 2(5) + 4 = 14 10 + 4 = 14 Do the math….. 14 = 14 

5x + 2 = 12 - 2 -2 5x = 10 5 5 x = 2 Try Another One… Addition Multiplication Addition 5x + 2 = 12 - 2 -2 Reverse order of operations says to undo addition (by subtracting) first… 5x = 10 5 5 Now undo multiplication (by dividing) x = 2

Check! Write original equation….. 5x + 2 = 12 Rewrite original equation with our answer….. 5(2) + 2 = 12 10 + 2 = 12 Do the math….. 12 = 12 

6x - 3 = 9 +3 +3 6x = 12 6 6 x = 2 Try Another One… Subtraction Multiplication Subtraction 6x - 3 = 9 +3 +3 Reverse order of operations says to undo subtraction (by adding) first… 6x = 12 6 6 Now undo multiplication (by dividing) x = 2

Check! Write original equation….. 6x - 3 = 9 Rewrite original equation with our answer….. 6(2) - 3 = 9 12 - 3 = 9 Do the math….. 9 = 9 

x 2 - 4 = 1 +4 +4 2 1 x 2 = 5 5 1 2 1 x = 10 Try Another One… Subtraction x 2 - 4 = 1 Division +4 +4 Reverse order of operations says to undo subtraction (by adding) first… 2 1 x 2 = 5 5 1 2 1 Now undo division (by multiplying) x = 10

Check! Write original equation….. x 2 - 4 = 1 10 2 Rewrite original equation with our answer….. - 4 = 1 5 - 4 = 1 Do the math….. 1 = 1 

x 3 + 1 = 3 - 1 - 1 3 1 x 3 = 2 2 1 3 1 x = 6 Try Another One… Addition x 3 + 1 = 3 Division - 1 - 1 Reverse order of operations says to undo addition (by subtracting) first… 3 1 x 3 = 2 2 1 3 1 Now undo division (by multiplying) x = 6

Check! Write original equation….. x 3 + 1 = 3 6 3 Rewrite original equation with our answer….. + 1 = 3 2 + 1 = 3 Do the math….. 3 = 3 