Sure, let's solve the equation step by step:
1. Start by distributing the 2 on the left side of the equation:
[tex]\[
2(3x - 1) = 6x - 2
\][/tex]
2. Next, distribute the -1 on the right side of the equation:
[tex]\[
5 - (x + 3) = 5 - x - 3 = 2 - x
\][/tex]
3. Now, set the left side equal to the right side:
[tex]\[
6x - 2 = 2 - x
\][/tex]
4. Combine like terms by adding x to both sides of the equation:
[tex]\[
6x + x - 2 = 2 - x + x
\][/tex]
5. Simplify:
[tex]\[
7x - 2 = 2
\][/tex]
6. Add 2 to both sides of the equation to isolate the terms with [tex]\(x\)[/tex]:
[tex]\[
7x - 2 + 2 = 2 + 2
\][/tex]
7. Simplify further:
[tex]\[
7x = 4
\][/tex]
8. Finally, divide both sides by 7 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{4}{7}
\][/tex]
Thus, the solution to the equation is:
[tex]\[
x = \frac{4}{7} \approx 0.5714285714285714
\][/tex]
