To solve the equation [tex]\(4(x+9) + 5 = 3x - 8\)[/tex] using the subtraction property of equality, we need to understand what this property means. The subtraction property of equality states that if you subtract the same number from both sides of an equation, the equation remains balanced and the equality is preserved.
Let's analyze each option provided:
1. [tex]\(4(x+9) - 5 + 8 = 3x\)[/tex]
In this option, we see an attempt to modify the original equation [tex]\(4(x+9) + 5 = 3x - 8\)[/tex]. However, this modification does not correctly apply the subtraction property of equality and introduces unnecessary operations on one side of the equation.
2. [tex]\(4(x+9) = 3x - 8 - 5\)[/tex]
This option shows that we have subtracted 5 from both sides of the original equation, correctly applying the subtraction property of equality. The equation remains balanced:
[tex]\[
4(x+9) + 5 - 5 = 3x - 8 - 5
\][/tex]
Simplifying it gives us:
[tex]\[
4(x+9) = 3x - 8 - 5
\][/tex]
This correctly demonstrates the subtraction property of equality step.
3. [tex]\(x = -49\)[/tex]
This option provides a specific value for [tex]\(x\)[/tex], but it does not relate to demonstrating the subtraction property of equality as applied to the given equation.
4. [tex]\(4x + 36 + 5 = 3x - 8\)[/tex]
This option represents a simplification or rearrangement, not applying the subtraction property of equality. It shows the distribution of [tex]\(4\)[/tex] over [tex]\((x+9)\)[/tex] and some extra algebraic steps, but it doesn't demonstrate subtracting the same value from both sides of the equation.
The correct option that indicates the subtraction property of equality when solving the equation [tex]\(4(x+9) + 5 = 3x - 8\)[/tex] is:
[tex]\[ 4(x+9) = 3x - 8 - 5 \][/tex]
So, the answer is [tex]\(\boxed{2}\)[/tex].
