Download Section 3.3 “Solving Equations with Variables on Both Sides”

Do Now 10/30/09
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Copy HW in your planner.
– Text p. 134, #12-28 evens & #34 & #36
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Objective
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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.
Section 3.3 “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.
To get all the ‘x’
variables on one
side “add 8x.”
7 – 8x = 4x – 17
+ 8x + 8x
7 = 12x – 17
+17
+17
24 = 12x
12 12
2=x
To get the “12x” by itself
“add 17” to both sides.
To get the ‘x’ by
itself “divide by 12”
to both sides.
Check Your Work!
7 – 8x = 4x – 17
x =2
7 – 8(2) = 4(2) – 17
Are both sides equal?
Practice
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1) 6x + 11 = 2x – 5
4x + 11 = -5
4x = -16
x = -4
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2) -17p – 6 = -38 – p
-16p – 6 = -38
-16p = -32
p=2
Solving Equations with Variables on
Both Sides…
Isolate the variable! Get ‘x’ by itself.
9x – 5 = 2(2x + 7.5)
9x – 5 = 2(2x + 7.5)
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 = 2 (2x + 7.5)
x =4
9(4) – 5 = 2 (2(4) + 7.5)
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
All Numbers
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
All numbers
No solution
Homework
Text p. 134, #12-28 evens & #34 & #36