Solving 2 Step Equations

Solving 2 Step Equations 1) Undo the addition or subtraction operation first, by using inverse operations. 2) Undo the multiplication or division operation second, by using inverse operations.

Solving 2 Step Equations To solve any equation, you want to get the variable all by itself. You get the variable alone by using inverse operations. Inverse Operations are like Opposites Addition and subtraction are inverses because addition will ‘undo’ subtraction. Multiplication and Division are inverses because multiplication will ‘undo’ division.

Solving 2 Step Equations 1) GOAL: Get the variable on one side of the equation. 2) You always perform the same operation to both sides of an equation. 3) To undo an operation you perform its opposite operation to both sides of the equation. 4) It is easier if you undo addition or subtraction before you undo multiplication or division.

Solving 2 Step Equations 3x + 4 = 16 3x + 4 = 16 Undo Addition or Subtraction 1st -4 -4 3x = 12 Then undo Mult. or Div. 2nd 3 3 x = 4

Solving 2 Step Equations 2x + 4 = 10 Get the variable alone. - 4 - 4 Subtract 4 from both sides. 2x = 6 __ __ 2 2 +4 and -4 cancel out Divide both sides by 2 x = 3 2 divided by 2 cancel to 1 2(3) +4 = 10 Check your answer by plugging it back into the original equation 6 + 4 = 10 It should ‘work’ (make a true statement) 10 = 10

Solving 2 Step Equations 3m - 10 = 17 Get the variable alone. + 10 +10 Add 10 to both sides. 3m = 27 __ __ 3 3 +10 and -10 cancel out Divide both sides by 3 m = 9 3 divided by 3 cancel to 1 3(9) – 10 = 17 Show your check. 27 – 10 = 17 Finish your check. 17 = 17

Solving 2 Step Equations x 3 – 4 = 8 Get the variable alone. +4 +4 Add 4 to both sides. x 3 = 12 + 4 and -4 cancel out. x 3 Multiply both sides by 3. 3 ( ) = 3 12 3 divided by 3 cancel to 1 x = 36 36 3 – 4 = 8 Show your check. 12 – 4 = 8 Finish your check. 8 = 8

Solving 2 Step Equations x 2 + 6 = 14 Get the variable alone. - 6 - 6 Subtract 6 from both sides. x 2 = 8 + 6 and -6 cancel out. x 2 Multiply both sides by 2. 2 ( ) = 2 8 2 divided by 2 cancel to 1 x = 16 16 2 + 6 = 14 Show your check. 8 + 6 = 14 Finish your check. 14 = 14

Solving 2 Step Equations What Operation Do You Do? FIRST SECOND 1) 3x + 8 = 24 Divide by 3 Subtract 8 2) 5x - 10 = 19 Divide by 5 Add 10 3) x - 4 = 20 2 Add 4 Multiply by 2 4) - 30 = -5x + 5 Divide by -5 Subtract 5

Solving 2 Step Equations

Solving 2 Step Equations

Solving 2 Step Equations Think about what you need to do to isolate the variable. Get rid of addition or subtraction first. Second get rid of multiplication or division.

EXPLANATION if you see the phrase ‘balance the equation’ or keep the equation “balanced”

An Equation is like a balance scale An Equation is like a balance scale. Everything must be equal on both sides. = 20 2x +5

What you do to one side of an equation, you must do to the other side to keep it balanced! = 20 2x +5 -5 -5

What you do to one side of an equation, you must do to the other side to keep it balanced! = 15 2x __ 2 __ 2

What you do to one side of an equation, you must do to the other side to keep it balanced! = 7.5 x

Try to solve this subtraction equation How do you get n all by itself? = 18 n - 3 +3 +3

Try to solve this subtraction equation How do you get n all by itself? = 21 n

Show your check by substituting your answer back into the original equation. = 18 21 n - 3

Try to solve this division equation How do you get x all by itself? x 3 = •3 •3 15

Try to solve this division equation How do you get x all by itself? x = 45

SHOW YOUR CHECK! 45 x 3 = 15