Algebra looks like a new language, but it is arithmetic with one change: some of the numbers are hidden behind letters. If you have ever filled in a blank like 7 + ___ = 12, you have already done algebra. This guide builds from that idea to solving two-step equations, with every example checked, and a practice set at the end.
A variable is a letter that stands for a number we don't know yet. In n + 7 = 12, the letter n is the number that makes the sentence true. Since 5 + 7 = 12, the answer is n = 5.
The letter itself doesn't matter. Mathematicians often use x, but n, a or t work just as well. Choosing a letter that means something, like t for the price of a ticket, can make word problems easier to follow.
When a number sits right next to a letter, it means multiply. So 3x means 3 times x, and if x is 4, then 3x is 12.
An expression is a calculation with no equals sign, like 3x + 4. You can simplify it or work it out for a given x, but you can't "solve" it.
An equation says two things are equal, like 3x + 4 = 19. Solving it means finding the value of x that makes both sides match.
In 3x + 4, the parts joined by + or − are called terms. The 3 in 3x is the coefficient, and the 4 on its own is a constant.
Like terms have exactly the same letter part, so they can be added together, just as 2 apples and 3 apples make 5 apples.
So the equation 2x + 3x = 10 becomes 5x = 10, and dividing both sides by 5 gives x = 2.
When an expression has several operations, the order matters. Work out brackets first, then powers, then multiplication and division, then addition and subtraction. Many schools use the memory aid PEMDAS or BODMAS.
The last point trips up a lot of people: PEMDAS lists M before D, but they are a pair, and so are addition and subtraction.
Think of an equation as a balanced scale. You can do anything you like to it, as long as you do the same thing to both sides. The goal is to get the letter on its own.
One step. For x + 9 = 15, take 9 from both sides, which leaves x = 6.
Two steps. For 3x + 4 = 19:
Check by putting 5 back in: 3 × 5 + 4 = 19. It matches, so x = 5 is right.
Letters on both sides. For 5x − 7 = 2x + 8, first take 2x from both sides to get 3x − 7 = 8. Add 7 to both sides to get 3x = 15, so x = 5. Check both sides: 5 × 5 − 7 = 18 and 2 × 5 + 8 = 18. They match.
Brackets. For 2(x + 3) = 14, multiply out the bracket to get 2x + 6 = 14. Take 6 from both sides, 2x = 8, so x = 4. Check: 2 × (4 + 3) = 14.
Undoing each step with its opposite (adding undoes subtracting, dividing undoes multiplying) is the same idea as the fact families children learn with small numbers.
Most real algebra starts as a sentence. Pick a letter for the unknown, write the sentence as an equation, solve it, and check the answer against the words.
Tickets. Three cinema tickets and a 5 snack cost 41 in total. What does one ticket cost? Let t be the ticket price: 3t + 5 = 41. Take 5 from both sides, 3t = 36, so t = 12. Check: 3 × 12 + 5 = 41.
Ages. Sam is 4 years older than Priya, and their ages add up to 30. Let p be Priya's age, so Sam is p + 4. Then p + p + 4 = 30, so 2p + 4 = 30, 2p = 26 and p = 13. Priya is 13 and Sam is 17. Check: 13 + 17 = 30.
Many mental maths tricks are algebra rules being used without the letters. Working out 99 × 7 as (100 − 1) × 7 = 700 − 7 = 693 is the rule that a(b − c) = ab − ac. Seeing this connection makes both skills stronger. Our guide to fast multiplication uses this rule a lot, and algebraic multiplication with Vedic Maths applies the same patterns to expressions with letters. When you are ready for squared and cubed terms, read linear, quadratic and cubic polynomials.
Solve each equation, then check your answer by putting it back in.
Answers and checks:
Finding a missing number is algebra in its simplest form, and Missing Number lets you practise it as a game. Quick arithmetic makes every algebra step easier, so keep it sharp in practice mode or with one of our free maths games.
Start with what a variable means, then the order of operations, then solving one-step equations like x + 9 = 15. Once those feel easy, move on to two-step equations and brackets.
An expression, like 3x + 4, has no equals sign; you can simplify it but not solve it. An equation, like 3x + 4 = 19, says two things are equal, and solving it finds the value of x.
Putting the answer back into the original equation shows at once whether both sides match. It catches sign mistakes and slips in arithmetic, and it takes only a few seconds.