Certainly! Let's solve the equation step by step.
We have the equation:
[tex]\[ 3(2x + 1) + x = 7x - 9 \][/tex]
### Step 1: Distribute the 3 in the equation
Distribute the 3 into the expression inside the parentheses:
[tex]\[ 3 \cdot 2x + 3 \cdot 1 + x = 7x - 9 \][/tex]
[tex]\[ 6x + 3 + x = 7x - 9 \][/tex]
### Step 2: Combine like terms on the left side
Combine the [tex]\(6x\)[/tex] and [tex]\(x\)[/tex] on the left side:
[tex]\[ 6x + x + 3 = 7x - 9 \][/tex]
[tex]\[ 7x + 3 = 7x - 9 \][/tex]
### Step 3: Simplify the equation
To isolate the variable terms, subtract [tex]\(7x\)[/tex] from both sides:
[tex]\[ 7x + 3 - 7x = 7x - 9 - 7x \][/tex]
[tex]\[ 3 = -9 \][/tex]
### Step 4: Analyze the resulting equation
We now have a statement [tex]\(3 = -9\)[/tex] which is clearly false.
### Conclusion
The false statement indicates that there is no value of [tex]\(x\)[/tex] that will satisfy the original equation. Therefore, the equation has no solution.
So, the solution to the equation is:
[tex]\[ \boxed{\text{No solution}} \][/tex]
