Algebra

Solve for x: 2x + 5 = 13

Step-by-step solution with explanation

Final Answer

x = 4

Step-by-step solution

1

Subtract 5 from both sides

We subtract 5 from both sides to get the term with x by itself. Whatever we do to one side of an equation, we must do to the other side to keep it balanced.
2

Simplify both sides of the equation

On the left side, +5 and -5 cancel out to zero, leaving just 2x. On the right side, 13 - 5 equals 8.
3

Divide both sides by 2

We divide both sides by 2 to get x alone. This undoes the multiplication by 2 that was happening to x.
4

Simplify to find the answer

2 divided by 2 equals 1, so we're left with 1x, which is just x. On the right, 8 divided by 2 equals 4.

Understanding this problem

Learning Insight

Solving equations is like unwrapping a present — you undo each operation in reverse order. The number 5 was added to 2x, so we subtract it first. Then x was multiplied by 2, so we divide by 2 to unwrap it completely. The key is keeping the equation balanced by doing the exact same thing to both sides every time.

Quick Tip

Always work backwards from the order of operations. Deal with addition and subtraction first, then handle multiplication and division. This 'unwrapping' order makes solving equations much faster.

Common Mistake

Students often subtract 5 from only one side of the equation, writing 2x = 13 - 5 instead of subtracting from both sides. Remember: an equation is like a balanced scale — whatever you do to one side, you must do to the other, or it breaks.