An equation is a balance.
Arithmetic usually asks you to calculate with known numbers. Algebra also lets you work with values you do not know yet. We represent an unknown value with a symbol, often a letter such as x.
Consider this equation. It says that an unknown number, increased by three, gives eight.
To find x, we need to undo the addition of three. Subtract three from both sides so that the equality remains true.
Eight minus three is five, so the unknown number is five. We can check the result by putting five back into the original equation.
Solve it one step at a time.
We know the total, but not the original number.
x + 3 = 8Subtract 3 from both sides. The left side becomes just x.
x + 3 − 3 = 8 − 3We get x = 5. Substituting five into the original equation gives 5 + 3 = 8.
x = 5Build your own equation.
Now try a more general equation: ax + b = c. Change any value below and watch the equation update. Notice how each coefficient affects the answer.
Equation explorer
Adjust a, b, and c. The solution and explanation update automatically.
Your turn.
Solve each equation yourself before checking your answer. If you get stuck, reveal a hint rather than jumping straight to the solution.
Solve: x + 7 = 12
Enter the value of x.
Build on what you know.
You have explored the basic idea behind solving a linear equation. The next step is to practise using these operations with different numbers and more involved expressions.