Marvelous Monday Let’s demonstrate “ON TASK” behavior Find Seat Sharpen pencil (if necessary) Open notebook write today’s date Write the following problems below and simplify 2x – 4x + 3(6x2 – 6) + 10 ½(6x – 10) + ¼ (24x + 12) 8x2 + 3x – 2 + 6x2 – 10 – 7x

Solving 2-step and multi-step Equations

Solving 2 Step Equations To solve an equation means to find every number that makes the equation true.

Steps for Solving Two-Step Equations Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation. Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation.

Opposite Operations Addition  Subtraction Multiplication  Division

Helpful Hints? Identify what operations are on the variable side. (Add, Sub, Mult, Div) “Undo” the operation by using inverse operation. Whatever you do to one side, you must do to the other side to keep equation balanced.

Solving 2 Step Equations In the equation, x is the number you add to 7 to get 15.

Solving 2 Step Equations What is the number? 8, of course. So we would write the solution x = 8

Examples of more one-step equations

Solving 2 Step Equations But in other equations, the solution is not so obvious.

Solving 2 Step Equations Many times we need a way to solve equations. Especially if there is more than one step to solve.

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 REMEMBER

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.

I am going to show you 2 ways to solve this equation. Solving 2 Step Equations I am going to show you 2 ways to solve this equation. 3x + 4 = 16 Hard way Easy way Undo Multiplication or Division 1st Undo Addition or Subtraction 1st

Solving 2 Step Equations Hard way Easy way Undo Multiplication or Division 1st Undo Addition or Subtraction 1st 3x + 4 = 16 3x + 4 = 16 3 3 -4 -4 3x 4 16 + = 3x = 12 3 3 3 3 3 4 16 x + = 3 3 x = 4 4 4 - - 3 3 12 x = 3 x = 4

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 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 Show your check. 6 + 4 = 10 10 = 10 Finish your check.

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 Show your check. 36 3 – 4 = 8 Finish your check. 12 – 4 = 8 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 Show your check. + 6 = 14 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.

#11 Review 1) Undo the addition or subtraction operation first, by using inverse operations. 2) Undo the multiplication or division second, by using inverse operations.

Homework!