Algebra

2x + 3 = 2x + 5

Step-by-step solution with explanation

Final Answer

No solution — the equation is a contradiction with no value of x that satisfies it.

Step-by-step solution

1

Write down the equation clearly

We start by looking at both sides. Notice that both sides have the exact same term, .
2

Subtract 2x from both sides

We subtract from both sides to try to isolate the variable. Whatever we do to one side, we must do to the other to keep the equation balanced.
3

Simplify both sides

The terms cancel out on both sides, leaving us with . This is a false statement — 3 never equals 5, no matter what is.
4

Conclude there is no solution

Because we ended up with a false statement (), there is no value of that makes this equation true. The equation is called a contradiction.

Understanding this problem

Learning Insight

When both sides of an equation have the same variable term, the variable cancels out. If what remains is a false statement (like ), the lines these equations represent are parallel — they never intersect, so there is truly no solution.

Quick Tip

If you ever cancel the variable and get two different numbers equal to each other, stop right there — the answer is automatically 'no solution.'

Common Mistake

Students often mistakenly say or try to divide both sides by the variable. Subtracting the variable term is the right move, and when it fully cancels to a false statement, the answer is no solution — not zero.