Download Solving Equations

Solving Equations
With Variables on Both Sides
(VOBS)
Medina
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Steps to solve
get the letter by itself
variable
1. Simplify on side of the equation using distributive
property then combining like terms.
2. Simplify the other side of equation using distributive
property then combining like terms.
3. Get the variable on one side of equationMOVE VARIABLE FIRST!!!!
To avoid negative move the smaller variable to the bigger variable
4. Use inverse operations (do/undo)
You may not have to do all the steps to solve the equation
“You know you are done solving when there is a
positive 1 in front of the variable.”
Medina
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Solving Equations with Justification
2x  6  4x  3x  9 Original problem
6x 6  3x  9 Combine like terms
To Solve:  3x
 3x Subtraction Property of
Equality
Simplify
3x  6  9
D U
•3
-6
+6
÷3
6 6
3x  15
3
3
1x  5
Addition Property of Equality
Simplify
Division Property of Equality
Check solution
Medina
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Solving Equations with Justification
Check:
x 5
2x  6  4x  3x  9
6x  6  3x  9
6 5   6  3 5   9
30 6  15  9
24  24
Medina
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Solving Equations with Justification
4  x  3  2x  3x  6 Original problem
4x 12  2x  3x  6Distributive Property
Combine like terms

12

3
x

6
6x
To Solve:
 3x Subtraction Property of
 3x
Equality
D U
Simplify

6
3
x

12
• 3 - 12
+12
÷3
 12  12
3x  18
3
3
1x   6
Subtraction Property
of Equality
Simplify
Division Property of Equality
Check answer
Medina
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Solving Equations with Justification
4  x  3  2x  3x  6
Check:
x  -6
4x  12  2x  3x  6
6x  12  3x  6
6 -6  12  3 - 6  6
-36  12 -18  6
24  24
Medina
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Solving Equations with Justification
5𝑥 − 6 − 𝑥 = 2 𝑥 − 7 Original problem
To Solve:
Property
5𝑥 −6 + 𝑥 = 2 𝑥 − 7 Distributive
on left side
5𝑥 − 6 + 𝑥 = 2𝑥 −14 Distributive Property
on right side
6𝑥 −6 = 2𝑥 − 14 Combine like terms
D U
Subtraction Property
−2𝑥
−2𝑥
of Equality
•4 +6
4𝑥 −6 = −14
-6 ÷4
Simplify
Property of
+ 6 + 6 Addition
Equality
4𝑥 = −8
Simplify
4
4 Division Property of Equality
Check answer
1 𝑥 = −2
Medina
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Solving Equations with Justification
5𝑥 − 6 − 𝑥 = 2 𝑥 − 7
5 −2 − 6 − −2
Check:
𝑥 = −2
= 2 −2 − 7
−10 − 6 +2 = 2 −9
−10 −
= −18
8
−18 = −18
Medina
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Solving Equations with Justification
7𝑥 − 49 + 4𝑥 = −2 𝑥 + 5 Original problem
To Solve:
Combine like terms
11𝑥 −49 = −2 𝑥 + 5 on left side
Distributive Property
−2𝑥
−10 on right side
11𝑥 − 49 =
+2𝑥
Addition Property of
+2𝑥
Equality
D U 13𝑥 −49 = −10
Simplify
• 13 + 49
Addition Property of
+ 49 + 49
- 49 ÷ 13
Equality
13𝑥 = 39
Simplify
13 Division Property of Equality
13
Check answer
1𝑥 = 3
Medina
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Solving Equations with Justification
7𝑥 − 49 + 4𝑥 = −2 𝑥 + 5
7 3 − 49 + 4 3 = −2 3 + 5
Check:
𝑥=3
21 −49 +12 = −2 8
−28 +12 = −16
−16 = −16
Medina
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Determining the number of solutions:
There are 3 possibilities
No solution
1 solution
Get the variable
by itself and the
variable equals a
value x=-1
Infinitely Many Solutions
The variables cancel out
but the values don’t
equal one another 8=10
There is only one
value that can replace
the variable that will
make the statement
(equation) true.
There is NO value
that can replace the
variable, that will
make the statement
(equation) true.
The variables cancel out
and the values equal one
another 10=10
Any value that will
replace the variable
will make the
statement (equation)
true.
Medina
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Solving Equations with VOBS
D U
•5
+9
2x  6  4x  3x  9
2x 6  3x  9
 2x
 2x
 6  5x  9
-9
÷5
1 solution
9
9
15 5x
5 5
 3  1x
Only -3 will make the statement true
Medina
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Solving Equations with VOBS
Determining the number of solutions:
3x  3  5x  8x  9
8x 3  8x  9
 8x
 8x
3  9
No solution
Ask yourself
does 3 = 9?
There is NO value of
“x” that will make the
statement true.
Medina
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Solving Equations with VOBS
Determining the number of solutions:
5  x  3  4x  9x  15
5x 15  4x  9x  15
9x 15  9x  15
 9x
 9x
-15  - 15
Infinite Solutions
Ask yourself
does -15 = -15?
Any value of “x” will make
the statement true.
Medina
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