Algebra

3(x + 1) = 3x + 3

Step-by-step solution with explanation

Final Answer

All real numbers (infinitely many solutions). Every value of satisfies this equation.

Step-by-step solution

1

Distribute 3 on the left side

Multiply 3 by each term inside the parentheses. This uses the distributive property: .
2

Simplify the left side

After distributing, the left side becomes . Now both sides look exactly the same.
3

Subtract 3x from both sides

We try to isolate x by removing the terms. Subtracting from both sides keeps the equation balanced.
4

Result is a true statement

The variable completely cancels out, and we are left with , which is always true no matter what is. This means every real number is a solution.

Understanding this problem

Learning Insight

When both sides of an equation are identical, the equation is called an identity. It is true for all real values of x, not just one specific value. This happens because the original equation had no new information — both sides were always equal.

Quick Tip

If you distribute and both sides become identical, stop right there — the answer is 'all real numbers.' No need to keep solving.

Common Mistake

Students often write 'no solution' when the variable cancels out. 'No solution' only happens when you get a FALSE statement like . A TRUE statement like means infinitely many solutions.