To solve the equation \(3 + 2x + 1 = 5 + 2x - 1\), follow these detailed steps:
1. Simplify both sides of the equation:
- Combine the constants on each side.
On the left side:
[tex]\[
3 + 2x + 1 = 4 + 2x
\][/tex]
On the right side:
[tex]\[
5 + 2x - 1 = 4 + 2x
\][/tex]
Therefore, the simplified equation is:
[tex]\[
4 + 2x = 4 + 2x
\][/tex]
2. Analyze the equation:
- Observe that both sides of the simplified equation are identical: \(4 + 2x = 4 + 2x\).
3. Isolate the variable:
- Subtract \(2x\) from both sides of the equation to simplify further:
[tex]\[
4 + 2x - 2x = 4 + 2x - 2x
\][/tex]
This simplifies to:
[tex]\[
4 = 4
\][/tex]
4. Conclusion:
- The statement \(4 = 4\) is always true, regardless of the value of \(x\). This means that the original equation holds for all values of \(x\).
Therefore, considering the above logical steps, the correct conclusion for the given equation is that there are no solutions.
