Do Now 6/10/13Do Now 6/10/13

Copy HW in your planner.Copy HW in your planner.– Text p. 478, #8-26 evens, & 30 Text p. 478, #8-26 evens, & 30 – Cumulative Test Chapters 1-11 Thursday Cumulative Test Chapters 1-11 Thursday – Benchmark Test next MondayBenchmark Test next Monday

ObjectiveObjective SWBAT solve equations with SWBAT solve equations with

variables on both sidesvariables on both sides

Equation-Equation-mathematical sentence mathematical sentence with an equal signwith an equal sign

Like a scale,Like a scale,both sides must be both sides must be EQUALEQUAL in order in order to be balanced.to be balanced.

Section 11.3 “Solving Equations Section 11.3 “Solving Equations with Variables on Both Sides”with Variables on Both Sides”

How can you get the “unknown” by How can you get the “unknown” by itself?itself?

Solving Equations with Variables on Both SidesSolving Equations with Variables on Both Sides

STEP 1- Use distributive property. STEP 1- Use distributive property. STEP 2- Combine like terms.STEP 2- Combine like terms.STEP 3- Collect variables on one side of the equation.STEP 3- Collect variables on one side of the equation.STEP 4- “Undo” addition and/or subtraction.STEP 4- “Undo” addition and/or subtraction.STEP 5- “Undo” multiplication and/or division.STEP 5- “Undo” multiplication and/or division.STEP 6- Solve for the variable.STEP 6- Solve for the variable.STEP 7- Check your work.STEP 7- Check your work.

7 - 8x = 4x – 177 - 8x = 4x – 17

7 – 8x = 4x – 17 7 – 8x = 4x – 17 + 8x + 8x

1212

7 = 12x – 17 7 = 12x – 17

To get all the ‘x’ To get all the ‘x’ variables on one variables on one side “add 8x.” side “add 8x.”

To get the “12x” by itselfTo get the “12x” by itself““add 17” to both sides.add 17” to both sides.

+17+17 +17 +17

24 = 12x24 = 12xTo get the ‘x’ byTo get the ‘x’ by itself “divide by 12” itself “divide by 12” to both sides.to both sides.

+ 8x + 8x

1212 2 = x2 = x

Check Your Work!Check Your Work!

xx = 2 = 2

7 – 8(7 – 8(22) = 4() = 4(22) – 17 ) – 17

Are both sides equal?Are both sides equal?

7 – 8x =7 – 8x = 4 4xx – 17 – 17

5x = 4x + 95x = 4x + 9

- 4x - 4x

1x = 9 1x = 9

To get all the ‘x’ To get all the ‘x’ variables on one variables on one side “subtract side “subtract 4/9x.” 4/9x.”

To get the “1/9x” by itselfTo get the “1/9x” by itself““multiply 9” to both sides.multiply 9” to both sides.

9 ∙9 ∙ ∙ ∙ 9 9

1x = 811x = 81

- 4x - 4x 9 9 9 9

9 9 9 9

9 9

9x – 5 = 4x + 15 9x – 5 = 4x + 15 -4x -4x

55

5x – 5 = 15 5x – 5 = 15

To get all the ‘x’ To get all the ‘x’ variables on one variables on one side “subtract 4x.” side “subtract 4x.”

To get the “5x” by To get the “5x” by itself “add 5” to both itself “add 5” to both sides.sides.

+ 5+ 5 + 5 + 5 5x = 205x = 20

To get the ‘x’ byTo get the ‘x’ by itself “divide by 5” to itself “divide by 5” to both sides.both sides.

-4x -4x

55 x = 4x = 4

9x – 5 = 2(2x + 7.5) 9x – 5 = 2(2x + 7.5) Distributive Distributive property property

8x + 32 = 65 + 5x 8x + 32 = 65 + 5x – – 5x 5x

33

3x + 32 = 65 3x + 32 = 65

To get all the ‘x’ To get all the ‘x’ variables on one variables on one side “subtract 5x.” side “subtract 5x.”

To get the “3x” by To get the “3x” by itself “subtract 32” itself “subtract 32” from both sides.from both sides.

- 32- 32 - 32 - 32 3x = 333x = 33

To get the ‘x’ byTo get the ‘x’ by itself “divide by 3” to itself “divide by 3” to both sides.both sides.

– – 5x 5x

33 x = 11x = 11

8(x + 4) = 5(13 + x) 8(x + 4) = 5(13 + x) Distributive Distributive property property

Geometry ConnectionGeometry ConnectionThe figures below have the same perimeter. The figures below have the same perimeter.

Find the perimeter. Find the perimeter.

x + 2 x + 2

x + 3 x + 3

= =

1x – 2 = 7 1x – 2 = 7

x = 9 x = 9 The perimeter of both The perimeter of both figures is 34 units. figures is 34 units.

-3x -3x-3x -3x

+2 +2+2 +2x + 2 x + 2

x x

x – 1 x – 1

4x – 2 = 3x + 7 4x – 2 = 3x + 7

1) 6x + 11 = 2x – 5 1) 6x + 11 = 2x – 5 2) -17p – 6 = -38 – p 2) -17p – 6 = -38 – p

4x + 11 = -5 4x + 11 = -5

4x = -16 4x = -16

x = -4 x = -4

-16p – 6 = -38 -16p – 6 = -38

-16p = -32 -16p = -32

p = 2 p = 2

PracticePractice

HomeworkHomework– Text p. 478, #8-26 evens, & 30Text p. 478, #8-26 evens, & 30– Cumulative Test Chapters 1-11 Thursday Cumulative Test Chapters 1-11 Thursday