This question tests solving linear equations with fraction/decimal coefficients using distributive property and combining like terms. The process involves distributing a(bx+c)=abx+ac (e.g., 2/3(x-6)=2x/3-4), collecting like terms (2x+3x=5x, 1/2x+1/4x=3/4x using common denominator), isolating the variable (move x terms one side, constants other), and solving (divide both sides); clearing fractions by multiplying by LCD simplifies arithmetic (equation with 1/2 and 3/4: multiply by 4 converts to integers). For the equation 0.6(x+5)-0.2x=4, distribute to get 0.6x + 3 - 0.2x = 4, combine x terms to 0.4x + 3 = 4, subtract 3 to get 0.4x = 1, and divide by 0.4 to find x=2.5. The correct process yields x=2.5, which matches choice B. A common error is mishandling the subtraction of 0.2x, such as treating it as addition, or decimal division errors. Steps: (1) clear fractions if desired (multiply by LCD), (2) distribute (remove parentheses), (3) collect like terms (combine x's, combine constants), (4) isolate x (add/subtract to get x terms one side, constants other), (5) divide (coefficient of x), (6) simplify (reduce fraction if needed), (7) check (substitute back). Common errors: distributing only first term, adding fractions without common denominator (1/2+1/3≠2/5), sign errors moving terms, dividing wrong (x/4=2 → x=8 not 0.5).

This question tests solving linear equations with fraction/decimal coefficients using distributive property and combining like terms. The process involves distributing a(bx+c)=abx+ac (e.g., 2/3(x-6)=2x/3-4), collecting like terms (2x+3x=5x, 1/2x+1/4x=3/4x using common denominator), isolating the variable (move x terms one side, constants other), and solving (divide both sides); clearing fractions by multiplying by LCD simplifies arithmetic (equation with 1/2 and 3/4: multiply by 4 converts to integers). For the equation 0.5(x+6) + 1.25 = 0.8x - 0.25, distribute to get 0.5x + 3 + 1.25 = 0.8x - 0.25, combine constants to 0.5x + 4.25 = 0.8x - 0.25, subtract 0.5x from both sides to get 4.25 = 0.3x - 0.25, add 0.25 to both sides to get 4.5 = 0.3x, and divide by 0.3 to find x=15. The correct process yields x=15, which matches choice C. A common error is mishandling decimals, such as subtracting 0.5 from 0.8 incorrectly as 0.2 instead of 0.3, or forgetting to add the constants properly. Steps: (1) clear fractions if desired (multiply by LCD), (2) distribute (remove parentheses), (3) collect like terms (combine x's, combine constants), (4) isolate x (add/subtract to get x terms one side, constants other), (5) divide (coefficient of x), (6) simplify (reduce fraction if needed), (7) check (substitute back). Common errors: distributing only first term, adding fractions without common denominator (1/2+1/3≠2/5), sign errors moving terms, dividing wrong (x/4=2 → x=8 not 0.5).

This problem tests solving linear equations with fraction/decimal coefficients using distributive property and combining like terms. Process: distribute a(bx+c)=abx+ac (2/3(x-6)=2x/3-4), collect like terms (2x+3x=5x, 1/2x+1/4x=3/4x using common denominator), isolate variable (move x terms one side, constants other), solve (divide both sides). Clearing fractions by multiplying by LCD simplifies arithmetic (equation with 1/2 and 3/4: multiply by 4 converts to integers). For this specific equation, distribute 2.5 to (x-1.2) to get 2.5x - 3, then subtract 0.5x yielding 2.5x - 0.5x - 3 = 6.4; combine to 2x - 3 = 6.4, add 3 to get 2x = 9.4, then divide by 2 to find x = 4.7 or 47/10. The correct process yields the answer x = 47/10. A common error is miscalculating the distribution like 2.5*1.2 as 2.5 instead of 3, leading to wrong values like 37/10. Steps: (1) clear fractions if desired (multiply by LCD), (2) distribute (remove parentheses), (3) collect like terms (combine x's, combine constants), (4) isolate x (add/subtract to get x terms one side, constants other), (5) divide (coefficient of x), (6) simplify (reduce fraction if needed), (7) check (substitute back). Common errors: distributing only first term, adding fractions without common denominator (1/2+1/3≠2/5), sign errors moving terms, dividing wrong (x/4=2 → x=8 not 0.5).

This problem tests solving linear equations with fraction/decimal coefficients using distributive property and combining like terms. Process: distribute $a(bx+c)=abx+ac$ ($\frac{2}{3}(x-6)=\frac{2x}{3}-4$), collect like terms ($2x+3x=5x$, $\frac{1}{2}x+\frac{1}{4}x=\frac{3}{4}x$ using common denominator), isolate variable (move x terms one side, constants other), solve (divide both sides). Clearing fractions by multiplying by LCD simplifies arithmetic (equation with $\frac{1}{2}$ and $\frac{3}{4}$: multiply by 4 converts to integers). For this specific equation, distribute $-\frac{1}{3}$ to (x-9) to get $-(\frac{1}{3})x + 3$, then add ($\frac{5}{6}$)x yielding ($\frac{5}{6}x - \frac{1}{3}x + 3 = 12$); combine to ($\frac{1}{2}x + 3 = 12$), subtract 3 to get ($\frac{1}{2}x = 9$), then multiply by 2 to find x = 18. The correct process yields the answer x = 18. A common error is distributing with the wrong sign, like subtracting instead of adding 3, leading to wrong values like x = 9. Steps: (1) clear fractions if desired (multiply by LCD), (2) distribute (remove parentheses), (3) collect like terms (combine x's, combine constants), (4) isolate x (add/subtract to get x terms one side, constants other), (5) divide (coefficient of x), (6) simplify (reduce fraction if needed), (7) check (substitute back). Common errors: distributing only first term, adding fractions without common denominator ($\frac{1}{2}+\frac{1}{3}\neq\frac{2}{5}$), sign errors moving terms, dividing wrong ($\frac{x}{4}=2 \rightarrow x=8$ not 0.5).

This question tests solving linear equations with fraction coefficients using combining like terms. Process: collect like terms ($ \frac{1}{2} x - \frac{5}{8} x = -\frac{1}{8} x $), isolate variable (move x terms one side, constants other), solve (divide both sides). Clearing fractions by multiplying by LCD 8 simplifies arithmetic (equation with 1/2, 3/4, 5/8, 1/4: multiply by 8 converts to integers). For the equation ($ \frac{1}{2} x + \frac{3}{4} = \frac{5}{8} x - \frac{1}{4} $), subtract ($ \frac{1}{2} x $) to get ($ \frac{3}{4} = \frac{1}{8} x - \frac{1}{4} $), add ($ \frac{1}{4} $) to get ($ 1 = \frac{1}{8} x $), multiply by 8 to find ($ x = 8 $). The correct process and answer is $ x = 8 $, verified by substitution: left ($ \frac{1}{2}(8) + 0.75 = 4 + 0.75 = 4.75 $), right ($ \frac{5}{8}(8) - 0.25 = 5 - 0.25 = 4.75 $). A common error is incorrect fraction addition, like $ \frac{3}{4} + \frac{1}{4} $ as $ \frac{3}{8} $. Steps: (1) clear fractions (multiply by 8: $ 4x + 6 = 5x - 2 $), (2) collect like terms, (3) isolate x (subtract 4x: $ 6 = x - 2 $, add 2: $ x=8 $), (4) check. Common errors: adding fractions without common denominator, sign errors moving terms, dividing wrong.

This problem tests solving linear equations with decimal coefficients using the distributive property. Process: distribute $1.5(x-2) = 1.5x - 3$, combine like terms ($1.5x - 0.75x = 0.75x$), isolate variable, solve. For $1.5(x-2) - 0.75x = 6$: distribute to get $1.5x - 3 - 0.75x = 6$, combine x terms to get $0.75x - 3 = 6$, add 3 to both sides to get $0.75x = 9$, divide by 0.75 to get $x = 12$. The correct answer is $x=12$. Common errors include arithmetic mistakes with decimals or forgetting to distribute the negative sign.

This problem tests solving linear equations with decimals in a real-world context about mixing solutions. Process: distribute 0.25(4x-8) = x - 2, combine constants, isolate variable, and solve. Starting with 0.25(4x-8) + 1.5 = 5.5, distribute to get x - 2 + 1.5 = 5.5. Simplify left side: x - 0.5 = 5.5. Add 0.5 to both sides: x = 6. Common errors include incorrect distribution (0.25 × 4x = x, not 0.25x) or decimal arithmetic mistakes. Steps: (1) distribute carefully with decimals, (2) combine constants, (3) isolate x, (4) check by substituting back: 0.25(4·6-8) + 1.5 = 0.25(16) + 1.5 = 4 + 1.5 = 5.5 ✓.

This problem tests solving linear equations with fraction coefficients using distributive property and combining like terms. Process: distribute a(bx+c)=abx+ac, collect like terms using common denominators, isolate variable by moving x terms to one side and constants to the other, then solve by dividing both sides. For this equation: distribute 3/4(x-8) = 3x/4 - 6, so the equation becomes 3x/4 - 6 + x/2 = 10. To combine x terms, find common denominator: 3x/4 + x/2 = 3x/4 + 2x/4 = 5x/4. The equation is now 5x/4 - 6 = 10, so 5x/4 = 16, giving x = 64/5. Common errors include distributing incorrectly (forgetting to multiply both terms) or adding fractions without finding common denominators.

This problem tests solving linear equations with multiple fractions requiring distribution and combining like terms. Process: distribute 1/4(2x-12) = x/2 - 3, combine all x terms and constants, then solve. Starting with 1/4(2x-12) + 3x/8 = 3, distribute to get x/2 - 3 + 3x/8 = 3. To combine x terms, find LCD of 2 and 8, which is 8: 4x/8 + 3x/8 = 7x/8. The equation becomes 7x/8 - 3 = 3. Add 3 to both sides: 7x/8 = 6. Multiply by 8/7: x = 48/7. Common errors include incorrect distribution of fractions or adding fractions without common denominators. Steps: distribute carefully, find LCD for combining terms, isolate variable, and simplify final answer.

This problem tests solving linear equations with fraction coefficients by clearing fractions using LCD. Process: multiply entire equation by LCD of 6 to eliminate fractions, then solve the resulting integer equation. To solve: $\frac{5}{6}x - \frac{1}{3} = \frac{1}{2}x + 3$ → multiply by 6: $5x - 2 = 3x + 18$ → $5x - 3x = 18 + 2$ → $2x = 20$ → $x = 10$. Let me verify: $\frac{5}{6}(10) - \frac{1}{3} = \frac{50}{6} - \frac{2}{6} = \frac{48}{6} = 8$, and $\frac{1}{2}(10) + 3 = 5 + 3 = 8$ ✓. The correct answer is x = 10. Steps: (1) identify LCD as 6, (2) multiply every term by 6, (3) simplify to get 5x - 2 = 3x + 18, (4) collect x terms on left, (5) collect constants on right, (6) divide by 2. Common errors: forgetting to multiply every term by LCD, arithmetic mistakes when clearing fractions.