Help!!!
We’re not in balance!

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 = 35
This 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.

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.

• 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!!!!!

If a = c . . . then If a = c . . . then a + b = c + b
Adding the same value to two equal quantities keeps the equation in balance.
a - b = c - b
Subtracting the same value from two equal quantities keeps the equation in balance.

x - 12 = 59 x - 3 = -2
+ 12 + 12 +3 +3
X = 71
Did you notice that we x = 1 variable??????
The opposites of
12 and -12 created a 0 pair.
Remember that x – 3 = -2 is really x + (-3) = -2
Using a +3 under the -3 makes a 0 pair!! x + 4 = -5
-4 -4 x = -9

n + 6 = 4
-6 -6__ n = -2 remember . . . .
4 – 6 = 4 + (-6) n + 8 = 3
-8 = -8 n = -5
5 = d + 1
-1 = - 1
4 = d
Yes, it matters what side the variable is on. Leave it on the side it starts on . . . for now.
c + (-4) = -5
+4 = +4 c = -1 c – 4 = -5
+4 +4 c = -1 side of the equal sign. The answer
(solution) will be on the opposite side.

Fred’s target heart rate is 130 beats/minute. This is 58 beats/ min more than his resting heart rate. 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 -58
72 = r

Cora measures her heart rate at 123 beats per minute.
This is 55 beats per minute more than her resting heart rate, 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 just getting an answer.

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 steps as 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)
(+5)=+5 +30 30 14 14
There is one type of problem where NO
CHOICE is given.
A rewrite is required!
The rewritten equation is the equation to solve!
- 27 = w - (-14)
-27 = w + 14
-14 = -14
-41 = w

Your 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 . . . .
= 328 We’re looking for the TV price.
179 = t - difference
179 = t - 328
+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
+ 4 + 4 - 12 -12 - 12 -12
+7 +7
31 = n n = 3 n = - 32
2 = n
Check?
15 = n - 4 n - 12 = -5 n – (-10) = 2 -25 = n - 17
+ 4 + 4
19 = n
+ 12 +12 n = 7 n + 10 = 2
- 10 -10 n = -8
+17 +17
-8 = n

A number added to -5 equals -15.
When you go from words to an n + (-5) = -15 equation, the order of the math
+5 +5 symbols may be different from the order of the words: n = -10 Ten fewer than n would be n – 10
Eight less than r is written as r – 8 n times 5 becomes 5n
50 = n – (-12)
50 = n + 12
-12 -12
38 = n
Fifty is equal to the difference in a number and negative 12.

• 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!!!!!