3.5 And 3.6 Solving Equations

Section 3.5: Solving Equations by Adding or Subtracting By Ms. Dewey-Hoffman October 2 nd , 2008 (Thursday)

Using Subtraction to Solve Equations.
Remember these? N + 27 = 10?
The reason we can solve this type of problem is because of the Subtraction Property of Equality.
Remember! Subtract the same number from each side of the equation.
This will keep things balanced.
Check your work by sticking your answer back in to the original problem.

Try This, Then Check:
Solve:
n + 4.5 = -9.7
- 4.5 -4.5
n + 0 = -14.2
n = -14.2
Now check:
-14.2 + 4.5 = -9.7
This statement is true.
n = -14.2

Try This, Then Check:
Solve:
x + 4.9 = 18.8
- 4.9 = - 4.9
x + 0 = 13.9
x = 13.9
Check!
13.9 + 4.9 = 18.8
This is a true statement.
x = 13.9

Subtraction Property of Equality
Instead of using mental math, especially for crazy decimals, we use the Subtraction Property of Equality to help us solve for unknown variables.
So…DON’T ASK ABOUT MENTAL MATH and NO EXCUSE FOR NOT SHOWING WORK!

Word Problem with Subtraction Property of Equality
A communications satellite is circling Earth. Find the approximate distance from the satellite to the moon.
239.9 Thousand Miles 22.3 Thousand Miles ???

Word Problem with Subtraction Property of Equality, Cont.
Our Equation looks like this: 22.3 + x = 239.9
22.3 is miles from Earth to Satellite.
X is the miles from Satellite to Moon.
239.9 is the miles from the Earth to Moon.
239.9 Thousand Miles 22.3 Thousand Miles ???

Word Problem with Subtraction Property of Equality, Solve.
22.3 + x = 239.9
-22.3 -22.3
0 + x = 217.6
239.9 Thousand Miles 22.3 Thousand Miles 218 Thousand Miles
0 + x = 217.6
X = 217.6 miles from Satellite to Moon.
Round: 218 thousand miles from Satellite to Moon.

Another Word Problem
A store’s cost (plus) markup is the price you pay for an item. Suppose a pair of shoes costs a store $35.48. You pay $70. Write and solve an equation to find the store’s markup.
Store pays $35.48 for a pair of shoes.
You pay $70.00
What is the markup (what the store adds) to the cost of the shoes to make it what you paid?

Shoe Store Markup
Store pays $35.48 for a pair of shoes.
You pay $70.00
What is the markup (what the store adds) to the cost of the shoes to make it what you paid?
$35.48 + M = $70.00
Go ahead and do it!
M = $34.54, is the markup the store puts on the shoes.
So, the store makes $34.54 profit off of your $70 purchase.

Using Addition Property of Equality to Solve Equations.
Remember! Add the same number from each side of the equation.
This will keep things balanced.
Check your work by sticking your answer back in to the original problem.

Sample Problem
K – 14.4 = -18.39
+ 14.4 = +14.4
K – 0 = -3.99
K = -3.99
N – 5.85 = 15.25
+ 5.85 = +5.85
N – 0 = 21.1
N = 21.1
-10 = C – 2.6
+2.6 +2.6
-7.4 = C – 0
-7.4 = C

Word Problem!
Danzel wrote a check for $76.85. His new account balance is $235.00. What was his previous balance?
Previous Balance - Check = New Balance Previous Balance $76.85 - = $235.00 + 76.85 + 76.85 Previous Balance = $311.85

Solving Equations by Multiplying or Dividing Decimals Section 3.6 By Ms. Dewey-Hoffman

Using Division to Solve Equations
Division undoes multiplication.
You can solve an equation involving multiplication by dividing.
0.9r = - 5.4
0.9 0.9
r = - 6
Now check it!
r = - 6
0.9r = - 5.4
0.9(-6) = -5.4

Word Problem
An oil field produces an average of 16.8 thousand barrels of crude oil per day. About how many days will it take to produce 200 thousand barrels?
Barrels Made In A Day X Number of Days = 200 Thousand Barrels 16.8 X Number of Days = 200 Thousand Barrels

Word Problem Barrels Made In A Day X Number of Days = 200 Thousand Barrels 16.8 X Number of Days = 200 Thousand Barrels  16.8  16.8 Number of Days = 11.904, round to 12 Days. It will take 12 days to make 200 barrels of oil.

Using Multiplication to Solve Equations
To solve an equation involving division, multiply each side by the same nonzero number.
M  -7.2 = -12.5
x –7.2 x –7.2
M = 90
Now Check!
M = 90
M  -7.2 = -12.5
90  -7.2 = -12.5
True Statement

When Solving Equations…
Do everything you just learned, but remember!
You’re trying to get the variable alone, by itself, on one side of the equal side.
Whatever is happening to your variable, you have to undo.
If its multiplying, you divide.
If its subtracting, you add.
If its adding, you subtract.
If its dividing, you multiply.

Assignment #18
Handout Practice 3.5 and 3.6, Both Sides, ALL.
Make sure you bring your notes tomorrow.

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3.5 And 3.6 Solving Equations

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3.5 And 3.6 Solving Equations — Presentation Transcript