To solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ 3x = 6x - 2 \][/tex]
Follow these steps:
1. Isolate the variable terms on one side:
To get all the [tex]\( x \)[/tex]-terms on the same side, subtract [tex]\( 3x \)[/tex] from both sides of the equation:
[tex]\[
3x - 3x = 6x - 3x - 2
\][/tex]
Simplifying this, we get:
[tex]\[
0 = 3x - 2
\][/tex]
2. Get the constant term on the other side:
Add 2 to both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
0 + 2 = 3x - 2 + 2
\][/tex]
Simplifying this, we get:
[tex]\[
2 = 3x
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{2}{3}
\][/tex]
So, the solution for the equation [tex]\( 3x = 6x - 2 \)[/tex] is:
[tex]\[ x = \frac{2}{3} \][/tex]
Numerically, this value is approximately:
[tex]\[ x = 0.6666666666666666 \][/tex]
