Download Solving Equations with Variables on Both Sides

Do Now 10/7/09
• Take out HW from Monday.
– Text p. 150-152, #4-42 even
• Copy HW in your planner.
– Text p. 157-158 #8-14 even, #18-26 even,
#38-44 even
– QUIZ 3.1- 3.4 Friday
Homework
Text p. 150-152, #4-42 even
•
•
•
•
•
•
•
•
•
•
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4) 3
6) -5
8) -5
10) -7
12) 2
14) 3
16) 5
18) C
20) 1
22) 5
24) 22
• 26) Multiply each side by
2, not 1/2: x = 9
• 28) 0.5
• 30) 0.1
• 32) 1.2
• 34) 5 1/3
• 36) a). 12 b). 2.5
• 38) 6 tickets
• 40) 8 minutes
• 42) a). y = 74.5 x + 750;
x = 21 squares
Squares
5
10
15
20
25
Cost
($$)
1122.50
1495
1867.50
2240
2612.50
Objective
• SWBAT solve equations with
variables on both sides
Equation• mathematical sentence
with an equal sign
Like a scale,
both sides must be
EQUAL in order
to be balanced.
Solving Equations with
Variables on Both Sides
How can you get the “unknown” by itself?
7 - 8x = 4x – 17
Solving Equations with Variables on Both Sides
STEP 1STEP 2STEP 3STEP 4STEP 5STEP 6-
Use distributive property and combine like terms.
Collect variables on one side of the equation.
“Undo” addition and/or subtraction.
“Undo” multiplication and/or division.
Solve for the variable.
Check your work.
Solving Equations with
Variables on Both Sides…
Isolate the variable! Get ‘x’ by itself.
7 – 8x = 4x – 17.
Write original equation.
7 – 8x + 8x = 4x – 17 + 8x Add 8x to each side.
7 = 12x – 17
Simplify each side.
24 = 12x
Add 17 to each side.
2=x
Divide each side by 12.
Check Your Work!
7 – 8x = 4x – 17
x =2
7 – 8(2) = 4(2) – 17
Are both sides equal?
Solving Equations with
Variables on Both Sides…
Isolate the variable! Get ‘x’ by itself.
1
9x – 5 = 4 (16x + 60).
9x – 5 =
1 (16x + 60).
4
Write original equation.
9x – 5 = 4x + 15
Distributive property
5x – 5 = 15
Subtract 4x from each side.
5x = 20
x=4
Add 5 to each side.
Divide each side by 5.
Check Your Work!
9x – 5 = ¼ (16x + 60)
x =4
9(4) – 5 = ¼ (16(4) + 60)
Are both sides equal?
Solving Equations with Variables on
Both Sides…If Possible
Isolate the variable! Get ‘x’ by itself.
2 – 15n = 5(-3n +2)
3x +10 – x = 2(x +5)
2 – 15n = -15n + 10
2x + 10 = 2(x+5)
2 – 15n +15n = -15n +15n + 10
2 = 10
No Solution
2x + 10 = 2x + 10
Identity
Guided Practice
• 1) 6x + 11 = 2x – 5
4x + 11 = -5
4x = -16
x = -4
• 2) -17p – 6 = -38 – p
-16p – 6 = -38
-16p = -32
p=2
Guided Practice
4 + 2x + 8 = 2(x + 6)
7p + 6 – 3p = -38 + 4p
2x + 12 = 2(x + 6)
2x + 12 = 2x + 12
4p + 6 = -38 + 4p
6 ≠ -38
Identity
All numbers
No solution
Geometry Connection
Find the area and perimeter of the square.
4x – 2
3x + 7
The area of the square is
34 x 34 which is 1156
square units.
4x – 2 = 3x + 7
4x – 3x = 7 + 2
x=9
The perimeter of the
square is 34(4) which is
136 units.
Homework
Text p. 157-158 #8-14 even, #18-26 even,
#38-44 even
Mid-Chapter 3 Quiz Friday