Algebra

2x+5=13

Step-by-step solution with explanation

Final Answer

Step-by-step solution

Identify the equation to solve

We need to find the value of x that makes this equation true. We'll isolate x by undoing the operations around it.

Subtract 5 from both sides

We subtract 5 from both sides to cancel out the +5 on the left. This keeps the equation balanced.

Simplify both sides

On the left, 5 - 5 = 0, so we're left with 2x. On the right, 13 - 5 = 8.

Divide both sides by 2

We divide both sides by 2 to get x alone. Whatever we do to one side, we must do to the other.

State the solution

Dividing gives us x = 4. This is the one and only solution to this linear equation.

Understanding this problem

Learning Insight

This is a two-step linear equation. The goal is always to get x alone on one side. We work backwards through the order of operations — undoing addition/subtraction first, then multiplication/division — because we're reversing what was done to x.

Quick Tip

Check your answer by plugging x = 4 back in: ✓. Always verify in about 5 seconds!

Common Mistake

Students often subtract 5 from the right side but forget to subtract it from the left side too, breaking the balance of the equation. Both sides must always be treated the same.