Transcript Solving Equations with Variables on Both Sides

Do Now 6/10/13

Copy HW in your planner.
– Text p. 478, #8-26 evens, & 30
– Cumulative Test Chapters 1-11 Thursday
– Benchmark Test next Monday
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.
Section 11.3 “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 6STEP 7-
Use distributive property.
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?
To get all the ‘x’
variables on one
side “subtract
4/9x.”
5x = 4x + 9
9
9
- 4x - 4x
9
9
9 ∙1x = 9 ∙ 9
9
1x = 81
To get the “1/9x” by itself
“multiply 9” to both sides.
Distributive
property
To get all the ‘x’
variables on one
side “subtract 4x.”
To get the “5x” by
itself “add 5” to
both sides.
9x – 5 = 2(2x + 7.5)
9x – 5 = 4x + 15
-4x
-4x
5x – 5 = 15
+5 +5
5x = 20
5
5
x=4
To get the ‘x’ by
itself “divide by 5” to
both sides.
Distributive
property
8(x + 4) = 5(13 + x)
8x + 32 = 65 + 5x
– 5x
– 5x
3x + 32 = 65
- 32 - 32
3x = 33
3
3
x = 11
To get all the ‘x’
variables on one
side “subtract 5x.”
To get the “3x” by
itself “subtract 32”
from both sides.
To get the ‘x’ by
itself “divide by 3” to
both sides.
Geometry Connection
The figures below have the same perimeter.
Find the perimeter.
x–1
=
4x – 2 = 3x + 7
-3x
-3x
x
x+2
x+2
x+3
1x – 2 = 7
+2
+2
x=9
The perimeter of both
figures is 34 units.
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
Homework
– Text p. 478, #8-26 evens, & 30
– Cumulative Test Chapters 1-11 Thursday