2.5 Addition and Subtraction Equations

2.5 Addition and Subtraction Equations

Help!!!We’re not in balance!

Help!!!We’re not in balance!

Before we begin…..Before we begin…..

I hope last year you did not use one step to solve an equation. By this I mean solving

n – 30 = 5 by writing 30 + 5 = 35This is not keeping the equation in balance.This would also not work on equations like this:2{(n – (-12)} = -12 So… we will practice the

correct process. This involves properties.

I hope last year you did not use one step to solve an equation. By this I mean solving

n – 30 = 5 by writing 30 + 5 = 35This is not keeping the equation in balance.This would also not work on equations like this:2{(n – (-12)} = -12 So… we will practice the

correct process. This involves properties.

Equation RequirementsEquation Requirements

You are required to use Properties of Equality when solving equations. No, I didn’t make up a new property. They are on p. 86 & 88 in your book.

In other words, whatever you do to one side of an equation MUST be done to the other side.

You are required to use Properties of Equality when solving equations. No, I didn’t make up a new property. They are on p. 86 & 88 in your book.

In other words, whatever you do to one side of an equation MUST be done to the other side.

What is our objective?

• Our objective is to use the properties of equality to solve equations.

• Writing equations and using the proper process is part of this objective.

• It’s about the PROCESS!!!!!

The Properties of EqualityThe Properties of Equality

If a = c . . . then

a + b = c + b

Adding the same valueto two equal quantitieskeeps the equation inbalance.

If a = c . . . then

a - b = c - b

Subtracting the same valuefrom two equal quantitieskeeps the equation inbalance.

Solving Equations . . .Discussion Solving Equations . . .Discussion

x - 12 = 59 x - 3 = -2 x + 4 = -5+ 12 + 12

X = 71 Did you notice that we

used an identity property to “isolate” the variable??????

The opposites of 12 and -12 created a 0 pair.

+3

+3

x = 1

Remember that x – 3 = -2 is really x + (-3) = -2Using a +3 under the -3 makes a 0 pair!!

-4 -4

x = -9

As a rewrite, the problem would be x + (-12) = 59 The same solvingstep would be used.

Practice and NotesPractice and Notes

n + 6 = 4 -6 -6__ n = -2

remember . . . . 4 – 6 = 4 + (-6)

n + 8 = 3 -8 = -8

Yes, it matters what side the variable is on. Leave it on the side it starts on . . . for now.

n = -5

Inverse operations will be used to “isolate the variable.” We want the variable on one side of the equal sign. The answer (solution) will be on the opposite side.

5 = d + 1-1 = - 1 4 = d

Get over the fact that the answers areobvious. It will not stay that way.

c + (-4) = -5 +4 = +4

c = -1

c – 4 = -5 +4 +4 c = -1

Application Health p. 87Fred’s target heart rate is 130beats/minute. This is 58 beats/min more than his resting heartrate. Find the resting heart rate.

Operational words???

Something is 58 beats more than something else………

Target Rate = 58 more than resting rate

130 = 58 + r -58 -5872 = r

Cora measures her heart rate at 123 beats per minute.This is 55 beats per minute more than her resting heartrate, r. Write and solve an equation to find Cora’s resting heart rate. Operational words???

“This” refers to the 123.

123 is 55 more than resting rate

123 = 55 + r-55 -55

68 = r

We are writing equations . . . Not justgetting an answer.

The choice is yours……b – 12 = -49 is the first example given on p. 88. You have a choice as to how you want to approach this equation. You can solve it as it is written, understanding that -12 is the same as + (-12), or you can choose to rewrite it as addition. b – 12 = -49 or b – 12 = -49 + 12 +12 b + (-12) = -49 b = -37 +12 +12

b = -37

Using the single sign option will save you many stepsas we move forward. Please try it.

y – 5 = 8 (+5)=+5

y = 13

p – 30 = 42 + 30 =+30

p = 72

98 = n - 14 +14 = +14

112= n

y + (-5) = 8 p + (-30) = 42 98 = n + (-14)

There is one type of problem where NO CHOICE is given.

- 27 = w - (-14)

A rewrite is required!

-27 = w + 14

The rewritten equation is the equation to solve!

(+5)=+5 +30 30 14 14

-14 = -14-41 = w

Application p. 88Your friend’s DVD player was $328 less than her television. If the DVD player’s price was $179, how much did the TV cost? Remember, we are writing a subtraction equation.The difference in the two is $328 . . . .

179 = t - difference

179 = t - 328

= - 328 We’re looking for the TV price.

+328 = + 328$507 = tv

t - 328 = 179 + 328 + 328 tv = 507

The paperback is $17 less than the hardcover book….

The paperback is $5 and we want to find the price of the hardback book, AFTER writing a subtraction equation.

h – 17 = 5 +17 +17 h = $22

Small Group Practice and Process Check!!!!!!!

27 = (-4) + n n + 12 = 15 n + 12 = -20 -5 = -7 + n

15 = n - 4 n - 12 = -5 n – (-10) = 2 -25 = n - 17

+ 4 + 431 = n

Check?

- 12 -12n = 3

- 12 -12n = - 32

+7 +7

2 = n

+ 4 + 419 = n

+ 12 +12n = 7

n + 10 = 2 - 10 -10

n = -8

+17 +17-8 = n

Writing and Solving EquationsWriting and Solving Equations

A number added to -5 equals -15.

n + (-5) = -15 +5 +5 n = -10

Fifty is equal to the difference in a number and negative 12.

50 = n – (-12) 50 = n + 12

-12 -12 38 = n

Writing in Math p. 88When you go from words to anequation, the order of the mathsymbols may be different fromthe order of the words:

Ten fewer than n would be n – 10Eight less than r is written as r – 8n times 5 becomes 5n

What was our objective?

• Our objective was to use the properties of equality to solve equations.

• Writing equations and using the proper process was part of this objective.

• It’s about the PROCESS!!!!!