Answer:
a. Subtraction property
b. Addition property and Multiplication property
Step-by-step explanation:
Given
[tex]5y = 25[/tex]
Solving (a): Which property is applied to [tex]5y-7 = 25-7[/tex]
The property applied is the subtraction property of inequality, and it states that:
If [tex]a = b[/tex]
Then
[tex]a - x = b - x[/tex]
So, in this case:
[tex]a = 5y, b = 25\ and\ x=7[/tex]
Solving (b): Other properties
1. The additive property of equality
If [tex]a = b[/tex]
Then
[tex]a + x = b + x[/tex]
So, the expression can be written as:
[tex]5y + 12 = 25 + 12[/tex]
When 12 is subtracted from both sides, the equation returns to the original
i.e.
[tex]5y + 12 - 12 = 25 + 12 - 12[/tex]
[tex]5y = 25[/tex]
2. The multiplication property of equality
If [tex]a = b[/tex]
Then
[tex]a * x = b * x[/tex]
So, the expression can be written as:
[tex]5y* 2 = 25 * 2[/tex]
[tex]10y = 50[/tex]
When both sides are divided by 2, the equation returns to the original
i.e.
[tex]\frac{10y}{2} = \frac{50}{2}[/tex]
[tex]5y = 25[/tex]
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