To solve the equation 2x + 3 = 9 + 3x – 1, we will first simplify both sides.
1. Start by combining like terms on the right side:
- 9 – 1 = 8
- So the equation becomes: 2x + 3 = 8 + 3x
2. Next, we will rearrange the equation to get all the terms involving x on one side and the constant terms on the other side:
- Subtract 2x from both sides:
- 3 = 8 + 3x – 2x
- This simplifies to: 3 = 8 + x
3. Now, we will isolate x:
- Subtract 8 from both sides:
- 3 – 8 = x
- Which simplifies to: -5 = x
4. Finally, we can write the solution as:
x = -5
To verify, we can substitute x = -5 back into the original equation:
- Left side: 2(-5) + 3 = -10 + 3 = -7
- Right side: 9 + 3(-5) – 1 = 9 – 15 – 1 = -7
Since both sides are equal, our solution is confirmed!