Alright, let's solve these equations step by step.
### Equation 1: [tex]\(7x + 9 = 3 + 9x\)[/tex]
1. Isolate the variable terms on one side: Start by moving all terms involving [tex]\(x\)[/tex] to one side of the equation. We can subtract [tex]\(9x\)[/tex] from both sides:
[tex]\[
7x + 9 - 9x = 3
\][/tex]
2. Simplify the equation: Combine like terms:
[tex]\[
7x - 9x + 9 = 3 \implies -2x + 9 = 3
\][/tex]
3. Isolate [tex]\(x\)[/tex]: Move the constant term on the left side to the right side by subtracting 9 from both sides:
[tex]\[
-2x = 3 - 9 \implies -2x = -6
\][/tex]
4. Solve for [tex]\(x\)[/tex]: Divide both sides by [tex]\(-2\)[/tex]:
[tex]\[
x = \frac{-6}{-2} \implies x = 3
\][/tex]
So, the solution to the first equation is [tex]\(x = 3\)[/tex].
### Equation 2: [tex]\(x + 1 = 2x - 7\)[/tex]
1. Isolate the variable terms on one side: We start by moving all terms involving [tex]\(x\)[/tex] to one side of the equation. We can subtract [tex]\(x\)[/tex] from both sides:
[tex]\[
x + 1 - x = 2x - 7 - x
\][/tex]
2. Simplify the equation: Combine like terms:
[tex]\[
1 = x - 7
\][/tex]
3. Isolate [tex]\(x\)[/tex]: Move the constant term on the right side to the left side by adding 7 to both sides:
[tex]\[
1 + 7 = x \implies x = 8
\][/tex]
So, the solution to the second equation is [tex]\(x = 8\)[/tex].
### Summary of Solutions
- For the equation [tex]\(7x + 9 = 3 + 9x\)[/tex], the solution is [tex]\(x = 3\)[/tex].
- For the equation [tex]\(x + 1 = 2x - 7\)[/tex], the solution is [tex]\(x = 8\)[/tex].
Thus, the solutions to the given equations are:
[tex]\[
x = 3 \quad \text{and} \quad x = 8
\][/tex]
