Alright, let's solve the equation [tex]\(2x = 2(x - 3)\)[/tex] step-by-step.
1. Start with the given equation:
[tex]\[
2x = 2(x - 3)
\][/tex]
2. Distribute the 2 on the right-hand side:
[tex]\[
2x = 2x - 6
\][/tex]
3. Next, we want to get all the terms involving [tex]\(x\)[/tex] on one side. Subtract [tex]\(2x\)[/tex] from both sides of the equation:
[tex]\[
2x - 2x = 2x - 2x - 6
\][/tex]
4. Simplify both sides. On the left-hand side, [tex]\(2x - 2x\)[/tex] reduces to 0:
[tex]\[
0 = -6
\][/tex]
5. Since we end up with [tex]\(0 = -6\)[/tex], which is a contradiction, this tells us that there is no value of [tex]\(x\)[/tex] that will satisfy the original equation.
Therefore, the equation [tex]\(2x = 2(x - 3)\)[/tex] has no solutions.
