Q. Solve the Equation: \( -3(x – 14) + 9x = 6x + 42 \)

Problem: Solve the equation \( -3(x – 14) + 9x = 6x + 42 \).

1. Distribute (use the distributive property):

   Multiply \(-3\) by each term inside the parentheses \( (x – 14) \).

   Computation: \( -3(x – 14) = -3\cdot x + (-3)\cdot(-14) = -3x + 42 \).

   After distribution the equation becomes \( -3x + 42 + 9x = 6x + 42 \).

2. Combine like terms on the left-hand side:

   Combine the \(x\)-terms \(-3x\) and \(9x\): \( -3x + 9x = 6x \).

   So the left-hand side simplifies to \(6x + 42\), giving the equation \( 6x + 42 = 6x + 42 \).

3. Compare both sides and attempt to isolate the variable:

   Subtract \(6x\) from both sides to try to isolate \(x\):

   Computation: \( 6x + 42 – 6x = 6x + 42 – 6x \) which yields \( 42 = 42 \).

   Alternatively, subtract \(42\) from both sides to obtain \( 6x = 6x \) and then \( 0 = 0 \) after subtracting \(6x\); both lead to a true identity.

4. Conclusion about solutions:

   Because the equation simplifies to a true statement that does not involve \(x\) (for example \(42 = 42\) or \(0 = 0\)), the original equation is an identity: it is true for every real number \(x\).

   Therefore the solution set is all real numbers, written as \( \mathbb{R} \) or \( (-\infty, \infty) \).

5. Quick verification (optional):

   Pick any value of \(x\), for example \(x = 0\):

   Left side: \( -3(0 – 14) + 9\cdot 0 = -3(-14) + 0 = 42.\)

   Right side: \( 6\cdot 0 + 42 = 42.\)

   Both sides match, consistent with the conclusion that every real \(x\) satisfies the equation.

Final answer: All real numbers (solution set \( \mathbb{R} \) or \( (-\infty, \infty) \)).