Question

solve for x.
$6(x - 1) = 9(x + 2)$
options:
$x = -3$
$x = -8$
$x = 8$
$x = 3$

Explanation:

Step1: Apply distributive property

Using the distributive property \(a(b + c)=ab+ac\), we expand both sides of the equation \(6(x - 1)=9(x + 2)\).
For the left - hand side: \(6(x - 1)=6\times x-6\times1 = 6x-6\)
For the right - hand side: \(9(x + 2)=9\times x+9\times2=9x + 18\)
So the equation becomes \(6x-6=9x + 18\)

Step2: Move variable terms to one side

Subtract \(6x\) from both sides of the equation \(6x-6=9x + 18\)
\(6x-6-6x=9x + 18-6x\)
Simplifying, we get \(-6 = 3x+18\)

Step3: Move constant terms to the other side

Subtract 18 from both sides of the equation \(-6 = 3x+18\)
\(-6-18=3x+18 - 18\)
Simplifying, we have \(-24 = 3x\)

Step4: Solve for x

Divide both sides of the equation \(-24 = 3x\) by 3
\(\frac{-24}{3}=\frac{3x}{3}\)
Which gives \(x=-8\)

Answer:

\(x = - 8\) (the option: \(x=-8\))