Given the three equations, let's determine their solutions and then arrange them in order from least to greatest.
Equation A:
[tex]\[ 5(x - 6) + 3x = \frac{3}{4}(2x - 8) \][/tex]
Equation B:
[tex]\[ 2.7(5.1x + 4.9) = 3.2x + 28.9 \][/tex]
Equation C:
[tex]\[ 5(11x - 18) = 3(2x + 7) \][/tex]
The solutions to these equations are:
- Solution for Equation A: [tex]\( x = 3.69230769230769 \)[/tex]
- Solution for Equation B: [tex]\( x = 1.48249763481552 \)[/tex]
- Solution for Equation C: [tex]\( x = \frac{111}{49} \approx 2.26530612244898 \)[/tex]
To arrange these solutions in order from least to greatest, we compare the numerical values:
- Equation B: [tex]\( x \approx 1.48249763481552 \)[/tex]
- Equation C: [tex]\( x \approx 2.26530612244898 \)[/tex]
- Equation A: [tex]\( x \approx 3.69230769230769 \)[/tex]
Thus, the order from least to greatest is:
[tex]\[ \text{Equation B} < \text{Equation C} < \text{Equation A} \][/tex]
So, the arrangement is:
[tex]\[
\boxed{\text{Equation B}} < \boxed{\text{Equation C}} < \boxed{\text{Equation A}}
\][/tex]
