To find which equations are equivalent to [tex]\(-\frac{1}{4}x + \frac{3}{4} = 12\)[/tex], we need to simplify and compare each provided option step by step.
### Option 1: [tex]\(\left(\frac{-4 x}{1}\right)+\frac{3}{4}=12\)[/tex]
Simplifying:
[tex]\[
-4x + \frac{3}{4} = 12
\][/tex]
This is not equivalent to the original equation because the coefficient of [tex]\(x\)[/tex] is [tex]\(-4\)[/tex] instead of [tex]\(-\frac{1}{4}\)[/tex].
### Option 2: [tex]\(-1 \left(\frac{x}{4}\right)+\frac{3}{4}=12\)[/tex]
Simplifying:
[tex]\[
-\frac{x}{4} + \frac{3}{4} = 12
\][/tex]
This is equivalent to [tex]\(-\frac{1}{4}x + \frac{3}{4} = 12\)[/tex].
So, this option is equivalent to the original equation.
### Option 3: [tex]\(\frac{-x+3}{4}=12\)[/tex]
Simplifying by multiplying both sides by [tex]\(4\)[/tex]:
[tex]\[
-x + 3 = 48
\][/tex]
This does not match the original equation ([tex]\(-\frac{1}{4}x + \frac{3}{4} = 12\)[/tex]) as the constants and coefficients do not match directly.
### Option 4: [tex]\(\frac{1}{4}(x+3)=12\)[/tex]
Simplifying by multiplying both sides by [tex]\(4\)[/tex]:
[tex]\[
x + 3 = 48
\][/tex]
This also does not match the original equation as the structure and coefficients do not align.
### Option 5: [tex]\(\left(\frac{-x}{4}\right)+\frac{3}{4}=12\)[/tex]
Simplifying:
[tex]\[
-\frac{x}{4} + \frac{3}{4} = 12
\][/tex]
This is equivalent to [tex]\(-\frac{1}{4}x + \frac{3}{4} = 12\)[/tex].
So, this option is equivalent to the original equation.
### Conclusion
The equations that are equivalent to [tex]\(-\frac{1}{4}x + \frac{3}{4} = 12\)[/tex] are:
Option 2: [tex]\(-1 \left(\frac{x}{4}\right) + \frac{3}{4} = 12\)[/tex]
Option 5: [tex]\(\left(\frac{-x}{4}\right) + \frac{3}{4} = 12\)[/tex]
Hence, the final result is:
[tex]\[
\boxed{2, 5}
\][/tex]
