To solve for [tex]\( x \)[/tex] in the equation [tex]\( 3x = 6x - 2 \)[/tex], follow these detailed steps:
1. Original Equation:
[tex]\[
3x = 6x - 2
\][/tex]
2. Move all terms involving [tex]\( x \)[/tex] to one side of the equation:
Subtract [tex]\( 6x \)[/tex] from both sides of the equation to isolate the [tex]\( x \)[/tex]-terms on one side:
[tex]\[
3x - 6x = -2
\][/tex]
3. Simplify the equation:
Combine like terms on the left side:
[tex]\[
-3x = -2
\][/tex]
4. Solve for [tex]\( x \)[/tex] by isolating [tex]\( x \)[/tex]:
Divide both sides of the equation by [tex]\(-3\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-2}{-3}
\][/tex]
5. Simplify the fraction:
Simplifying [tex]\(\frac{-2}{-3}\)[/tex] gives:
[tex]\[
x = \frac{2}{3}
\][/tex]
Hence, the value of [tex]\( x \)[/tex] is:
[tex]\[
x = \frac{2}{3} \approx 0.6667
\][/tex]
