Solve for x

Attempts 0 of 6 Time 0:00

Statistics

Algebra

Solved by difficulty

Lattice

Solved by difficulty

Formula book

Keep it balanced

An equation is like a set of scales. Whatever you do to one side, do exactly the same to the other, and it stays true.

x + 4 = 10subtract 4 from both sidesx = 6

Undo with the opposite

To get x on its own, undo what's been done to it using the inverse operation.

You seeDo this to both sides
x + 5Subtract 5
x − 5Add 5
5xDivide by 5
x5Multiply by 5

Reading the notation

5x means 5 × x. A number written in front of a bracket multiplies everything inside it, so 3(x + 2) means 3 × (x + 2). A fraction line means divide: x4 is x ÷ 4.

Order of operations (BIDMAS)

Calculations happen in this order: Brackets, Indices, Division and Multiplication, Addition and Subtraction. When solving, undo them in reverse: deal with adding and subtracting first, then multiplying and dividing, then brackets.

2x + 3 = 11subtract 3 first, then divide by 2x = 4

Brackets

Either divide both sides by the number outside the bracket, or expand it by multiplying each term inside:

a(b + c) = ab + acfor example3(x + 4) = 3x + 12

A minus sign in front of a bracket changes every sign inside: −(x + 3) = −x − 3, and −2(x − 5) = −2x + 10.

Square brackets are just brackets. They're used when one bracket sits inside another, and you work from the outside in.

4[5(x − 3) + 8] = 212divide by 4 first5(x − 3) + 8 = 53

Collecting like terms

Terms with x combine with each other, and plain numbers combine with each other.

4x + 7 + 2x = 6x + 7

x on both sides

Subtract the smaller x term from both sides, so x only appears once.

5x + 2 = 3x + 10subtract 3x from both sides2x + 2 = 10

Fractions

Multiply both sides by the number on the bottom to clear the fraction. With more than one fraction, multiply by the lowest common denominator: the smallest number they all divide into.

x + 32 = 5multiply both sides by 2x + 3 = 10
x2 + x3 = 5multiply both sides by 63x + 2x = 30

Negative numbers

Two minuses multiplied or divided make a plus. Dividing a negative by a negative gives a positive answer.

−3x = −12divide both sides by −3x = 4

Check your answer

Put your value of x back into the original equation. If both sides come out the same, you're right.

3(x + 4) = 21 with x = 33 × 7 = 21✓

How to play Lattice

Lattice multiplication (sometimes called Chinese multiplication) lays a long multiplication out as a grid. Each puzzle is a multiplication with some digits hidden. Fill in every ?.

The grid

One number runs along the top and the other down the right side. Each cell holds its column digit times its row digit, split by the diagonal: tens in the top left, units in the bottom right. Here's 47 × 36:

The top-left cell is 4 × 3 = 12, so it shows 1 and 2. The bottom-right cell is 7 × 6 = 42.

Adding the diagonals

Start at the bottom right and add the digits in each diagonal band. Write the units digit in the box where the band ends, and carry any tens into the next band. The small number in a box's corner is the carry.

For 47 × 36: the corner is 2. The next band is 4 + 4 + 1 = 9. Then 2 + 2 + 2 = 6, then 1. Reading down the left and along the bottom gives 1692.

Solving a puzzle

Everything is connected, so work from what you can see. A few things that help:

Look at units digits. Anything times 5 ends in 0 or 5, and an even digit times anything gives an even result. If you know a cell and one of its two digits, the other is usually pinned down.

A cell's tens digit tells you roughly how big the product is: 2 × ? in the 10s means ? is 5 or more.

Product digits work backwards too. If a diagonal must end in 8 and you know all but one of its digits, you can work out the last one.

When two options both fit the grid, try each one. Only one will make every other digit, including the product, work.

The rules

Neither number starts with 0, and the product never starts with 0. Every puzzle has exactly one solution.

Difficulty

LevelPuzzleHints
Easy3-digit × 2-digit, a few digits hidden3
Medium4-digit × 3-digit, under half hidden4
Hard4-digit × 3-digit, most hidden. May need you to try options once5
Extreme4-digit × 3-digit, nearly everything hidden. May need it twice6

The daily lattice gets harder through the week: easy on Monday, medium Tuesday and Wednesday, hard Thursday and Friday, extreme at the weekend. Missed one? Play it from the archive. Practice gives unlimited puzzles at any level. Archive and practice puzzles don't affect your streak or statistics.

Tap a ? and use the number keys. Tap a cell to highlight its row and column digits, or a product box to highlight its diagonal. The small corner of each product box is for your own carry notes and isn't checked.

Check marks wrong digits in red, as often as you like. Each hint fills in the next digit you could work out and explains why. Revealing the solution counts as not solved.

How to play

Every day there is one new equation. Work out the value of x and enter it. You get 6 attempts, and x is always a whole number.

7(x + 4) = 42  gives  x = 2

Puzzles get harder through the week: easy on Monday, medium Tuesday and Wednesday, hard Thursday and Friday, expert at the weekend.

Stuck? Each hint reveals the next step of the working, and uses one of your attempts. Hints never give away the final answer. The formula book (the book icon) explains the rules for free.

When you finish, you'll see the worked solution. Solve on consecutive days to build a streak.

A new puzzle goes live at midnight in your time zone. Missed one? Play it from the archive. Archive puzzles don't affect your streak or statistics.

Practice gives you unlimited puzzles at any level. They don't count towards your statistics either.

Lattice is a second game: a multiplication grid with missing digits. Switch to it at the top. Its guide (the book or ? icon while you're in Lattice) explains how it works.