Transcript Solve Equations With Variables on Both Sides

Solve Equations With
Variables on Both
Sides
Example 1
• 3x + 4 = 5x – 8
• Since the x’s are on opposite sides of
the equal sign, you must “get rid” of
one of them by using inverse
operations.
• I like to “get rid” of the one on the right
side so that the x ends up on the left
side.
• So, I will subtract 5x from both sides.
Example 1
• 3x + 4 = 5x – 8
• 3x – 5x + 4 = 5x – 5x – 8 Simplify
• -2x + 4 = -8 Now you can solve this
equation!
• Subtract 4 from both sides.
• -2x + 4 – 4 = -8 – 4
• -2x = -12 Divide both sides by –2
• X=6
Example 2
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4(1 – 2x) = 4 – 6x
4 – 8x = 4 – 6x
4 – 8x + 6x = 4 – 6x + 6x
-2x + 4 = 4
-2x + 4 – 4 = 4 – 4
-2x = 0
X=0
Example 3
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9 + 5x = 5x + 9
9 + 5x – 5x = 5x + 9 – 5x
9=9
Since all of the variables are gone, this is
different.
• Does 9 = 9?
• Yes, so it is what we call an Identity (that
means there are infinitely many answers).
• So, the answer is all real numbers (R).
Example 4
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6x – 1 = 6x – 8
Subtract 6x from both sides.
6x – 6x – 1 = 6x – 6x – 8
-1 = -8
Again, both variables are gone. Is –1 = -8
true?
• No, so it is no solution (There aren’t any
numbers that will work.)
• The answer is no solution or 
From tonight’s work…
• #33 Justin and Tyson are beginning
an exercise program to train for
football season. Justin weighs 150 lb
and hopes to gain 2 lb per week.
Tyson weighs 195 lb and hopes to
lose 1 lb per week.
• If the plan works, in how many weeks
will the boys weigh the same?
Another one…
• Rapid Rental Car company charges a $40 rental
fee, $15 for gas, and $0.25 per mile driven. For
the same car, Capital Cars charges $45 for rental
and gas and $0.35 per mile.
• A. Find the number of miles for which the
companies’ charges will be the same.
• B. The Barre family estimates that they will drive
about 95 miles during their vacation. Which
company should they choose?
• C. If they extend their vacation and travel about
120 miles. Should they rent from the same
company?
Try these…
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2x + 16 = x – 25
14 – (2x + 5) = -2x + 9
0.7m = 0.9m + 2.4 – 0.2m
x + 1 = 4x + 1
5(x+7) = 2(x - 20) + x
Try these…-answers
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2x + 16 = x – 25
x = -41
14 – (2x + 5) = -2x + 9
R
0.7m = 0.9m + 2.4 – 0.2m

x + 1 = 4x + 1
x=0
5(x+7) = 2(x - 20) + x
x = -37.5