Algebra

2x + 5 = 11

Step-by-step solution with explanation

Final Answer

Step-by-step solution

Identify the goal: isolate x

We want to get x alone on one side of the equation. We do this by undoing each operation around x one step at a time.

Subtract 5 from both sides

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

Simplify both sides

On the left, 5 - 5 = 0, so we're left with 2x. On the right, 11 - 5 = 6.

Divide both sides by 2

We divide both sides by 2 to undo the multiplication. This leaves x completely alone on the left side.

State the final solution

6 divided by 2 equals 3. This is the one and only solution to this equation.

Understanding this problem

Learning Insight

This is a two-step linear equation. The big idea is 'inverse operations' — every math operation has an opposite that undoes it. Addition is undone by subtraction; multiplication is undone by division. We peel away operations in reverse order (like taking off layers) until x is alone.

Quick Tip

Work backwards using PEMDAS in reverse: undo addition/subtraction first, then undo multiplication/division. Think of it as unwrapping a gift — remove the outer layer before the inner one.

Common Mistake

A common mistake is dividing by 2 first before subtracting 5, which gives the wrong result. Always remove the constant term (the plain number) before dividing by the coefficient next to x.