Certainly! Let's solve the equation [tex]\( 3 - 4x = -5 \)[/tex] using deductive reasoning and properties of equality. We will go through the steps methodically.
1. Original Equation:
[tex]\[ 3 - 4x = -5 \][/tex]
2. Subtract 3 from both sides:
To isolate the term containing [tex]\( x \)[/tex], we first need to get rid of the constant term on the left side of the equation. By subtracting 3 from both sides, we get:
[tex]\[ 3 - 4x - 3 = -5 - 3 \][/tex]
This simplifies to:
[tex]\[ -4x = -8 \][/tex]
3. Divide by -4:
Now, we need to solve for [tex]\( x \)[/tex] by isolating it. Since [tex]\( x \)[/tex] is multiplied by [tex]\(-4\)[/tex], we divide both sides of the equation by [tex]\(-4\)[/tex]:
[tex]\[ \frac{-4x}{-4} = \frac{-8}{-4} \][/tex]
Simplifying both sides, we obtain:
[tex]\[ x = 2 \][/tex]
Conclusion:
The solution to the equation [tex]\( 3 - 4x = -5 \)[/tex] is [tex]\( x = 2 \)[/tex].
