Sure! Let's solve the equation step by step:
The given equation is:
[tex]\[ 3x - 5 = 2(x - 3) + x \][/tex]
1. Distribute the 2 on the right-hand side:
[tex]\[ 3x - 5 = 2x - 6 + x \][/tex]
2. Combine like terms on the right-hand side:
[tex]\[ 3x - 5 = 3x - 6 \][/tex]
3. Subtract [tex]\(3x\)[/tex] from both sides of the equation:
[tex]\[ 3x - 5 - 3x = 3x - 6 - 3x \][/tex]
[tex]\[ -5 = -6 \][/tex]
We end up with [tex]\(-5 = -6\)[/tex], which is a contradiction.
This result shows that the original equation has no solution. Therefore, there is no value of [tex]\(x\)[/tex] that will satisfy the given equation. The equation is inconsistent, meaning that it is impossible to find any real number [tex]\(x\)[/tex] that will make both sides of the equation equal.
The final answer is:
There is no solution.
