Answer :
To solve the equation [tex]\( c + 5 = 78 \)[/tex], we need to isolate the variable [tex]\( c \)[/tex]. The goal is to get [tex]\( c \)[/tex] by itself on one side of the equation.
### Step-by-Step Solution:
1. Identify the current equation:
[tex]\[ c + 5 = 78 \][/tex]
2. Determine what operation is currently being applied to [tex]\( c \)[/tex]:
In this case, [tex]\( 5 \)[/tex] is being added to [tex]\( c \)[/tex].
3. Determine the inverse operation needed to isolate [tex]\( c \)[/tex]:
To isolate [tex]\( c \)[/tex], we need to undo the addition of [tex]\( 5 \)[/tex] by using the inverse operation, which is subtraction.
4. Apply the Subtraction property of equality:
We subtract [tex]\( 5 \)[/tex] from both sides of the equation to maintain equality.
[tex]\[ c + 5 - 5 = 78 - 5 \][/tex]
5. Simplify both sides:
On the left side, [tex]\( 5 - 5 \)[/tex] cancels out, leaving [tex]\( c \)[/tex]:
[tex]\[ c = 78 - 5 \][/tex]
Simplify the right side:
[tex]\[ c = 73 \][/tex]
Thus, the property of equality that should be used to solve the equation [tex]\( c + 5 = 78 \)[/tex] is the Subtraction property of equality.
### Step-by-Step Solution:
1. Identify the current equation:
[tex]\[ c + 5 = 78 \][/tex]
2. Determine what operation is currently being applied to [tex]\( c \)[/tex]:
In this case, [tex]\( 5 \)[/tex] is being added to [tex]\( c \)[/tex].
3. Determine the inverse operation needed to isolate [tex]\( c \)[/tex]:
To isolate [tex]\( c \)[/tex], we need to undo the addition of [tex]\( 5 \)[/tex] by using the inverse operation, which is subtraction.
4. Apply the Subtraction property of equality:
We subtract [tex]\( 5 \)[/tex] from both sides of the equation to maintain equality.
[tex]\[ c + 5 - 5 = 78 - 5 \][/tex]
5. Simplify both sides:
On the left side, [tex]\( 5 - 5 \)[/tex] cancels out, leaving [tex]\( c \)[/tex]:
[tex]\[ c = 78 - 5 \][/tex]
Simplify the right side:
[tex]\[ c = 73 \][/tex]
Thus, the property of equality that should be used to solve the equation [tex]\( c + 5 = 78 \)[/tex] is the Subtraction property of equality.
