Algebra

2x + 5 = 13

Step-by-step solution with explanation

Final Answer

Step-by-step solution

Identify the equation to solve

We want to find the value of x that makes both sides equal. We'll isolate x by undoing each operation around it.

Subtract 5 from both sides

We subtract 5 from both sides to cancel the +5. Whatever we do to one side, we must do to the other to keep the equation balanced.

Simplify both sides

On the left, +5 and -5 cancel out. On the right, 13 - 5 = 8. Now x is almost alone.

Divide both sides by 2

We divide both sides by 2 to undo the multiplication. This fully isolates x.

State the solution

8 divided by 2 is 4. This is the one and only solution to this linear equation.

Understanding this problem

Learning Insight

A linear equation has exactly one solution because the variable appears only to the first power. The process of solving it is like peeling layers — you undo addition/subtraction first, then multiplication/division, working from the outside in toward x.

Quick Tip

Check your answer by plugging it back in: ✓. This takes 5 seconds and guarantees you're right.

Common Mistake

Students often subtract 5 from the left side but forget to subtract 5 from the right side too, breaking the balance of the equation and getting a wrong answer.