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Solving Equations with Variables on Both Sides
Transcript of Solving Equations with Variables on Both Sides
Application The long-distance rates of two phone companies are shown in the table. Phone Co. Charges Company A 36 cents plus 3 per min
Company B 6 cents per min Application (part two) "When is 36 cents plus 3 cents per minute
the same as 6 cents per minute?" To solve this problem we need to break it down. Let's sum up what we have into one sentence: Now what can we do with this? Answer: Let's make it an algebraic expression.
Then, we can solve for the missing piece Application (part three) When
cents plus 3 cents
per minute the same
as 6 cents
per minute ? Now that we have an algebraic equation,
we can solve for m... Solving with Variables on Both Sides Answer: Let's make it an algebraic expression.
Then, we can solve for the missing piece Get like terms
onto one side
and combine. Then solve
just like any
other equation. m = 12 A call 12 minutes
long will be the same
price on either company. ? ? ? Identity (Infinitely Many Solutions) Consider this: Condradiction (No Solutions) Also observe what happens here:
x + 4 - 6x = 6 - 5x - 2
Notice anything strange? Since this equation is ALWAYS true
for ANY value of x, it is called an
and has infinitely many solutions. identity For an identity,
all real numbers
-8x + 6 + 9x = -17 + x
Since this equation is NEVER true
for ANY value of x, it is called a
and has no solutions. contradiction For a contradiction,
there is no value of x
that will make the
equation true. OTHER EXAMPLES 7k = 4k + 15 k = 5 5x - 2 = 3x + 4 x = 3 2(y + 6) = 3y y = 12 3 - 5b + 2b = -2 - 2(1 - b) b = 1.4 Don't forget:
CHECK YOUR WORK!
MARK YOUR ANSWERS! Bell Ringer 1.) The sum of 5 and a number is 6.
2.) Two less than a number is -5.
3.) A number multiplied by negative 3 is 12.
4.) A number divided by 10 is equal to 40.
5.) Seven less than twice a number is 19. Solve: Assignment
pg. 103-104 15-19, 34-36, 51-52 ? Variables Both Sides How long is a call that costs the same amount no matter which company is used? What is the cost of that call? 36 + 3m = 6m -3m -3m 36 + 3m = 6m 36 = 3m 12 = m 3 3 So... Now, what does this mean? How do we figure out how
much the call would cost? We just have to substitute, or "plug in"
the value, 12, for the variable, m, into either side of the equation... 36 + 3m = 6m 12 12 36 + 3(12) = 72 6(12) = 72 *Notice they are both
the same value. *That's how we know
we got it right. 4 - 5x = 4 - 5x +5x +5x 4 = 4 This equation will be true no matter what we plug in for x. 6 + x = -17 + x - x - x 6 = -17 WHAT?! This obviously isn't true, and nothing we put in for x can change that...