Solve for $x$: $6(x-1)=9(x+2)$.

• A. $x=-8\frac{2}{3}$
• B. $x=8\frac{2}{3}$
• C. $x=-8\frac{1}{2}$
• D. $x=-8$

Answer: (A)

Verified step by step guidance

1. Start with the given equation: \$6(x - 1) = 9(x + 2)$.
2. Apply the distributive property to both sides: multiply 6 by each term inside the parentheses on the left, and 9 by each term inside the parentheses on the right. This gives \$6x - 6 = 9x + 18$.
3. Next, collect all terms containing \(x\) on one side and constant terms on the other side. For example, subtract \$6x$ from both sides and subtract 18 from both sides to isolate the variable terms.
4. Simplify the resulting equation to get an expression in the form \(ax = b\), where \(a\) and \(b\) are constants.
5. Finally, solve for \(x\) by dividing both sides of the equation by the coefficient \(a\).