Balance one-step, two-step and both-sides equations in your head against a ninety-second clock
Solve for X is an equation game: a linear equation appears, you balance it in your head and type the value of x. One Step deals equations such as x + 7 = 15 or 4x = 28, Two Steps adds a number to undo first, as in 3x − 5 = 16, and Both Sides puts x on each side of the equals sign or behind a bracket, as in 5x + 3 = 2x + 18. Every equation is built backwards from a whole-number answer, so there is always one clean solution to find, and a miss shows the answer with the first move that would have got you there.
Choose a level: One step, Two steps or Both sides.
Press Start. You have ninety seconds.
Work out x without writing anything down, then type it on the pad or your keyboard. Use the minus key for a negative answer.
Press Check or Enter. A right answer moves straight on; a wrong one shows the value of x and the first move to make.
Answer quickly for a bonus and keep a streak going to raise the multiplier.
When time runs out, the equations you missed are listed with their first moves, so you can see where each one turned.
Each equation is worth 10 points for every inverse operation it needs: one for x + 7 = 15, two for 3x − 5 = 16 or a bracket such as 3(x − 2) = 21, and three when x is on both sides. Answering within four seconds per step adds 5 points.
The total for each answer is multiplied by your streak multiplier, which starts at ×1 and goes up by one after every five right answers in a row, to a maximum of ×4. A wrong answer scores nothing and resets the streak. The round is ninety seconds, and the best score is saved separately for each level in this browser.
The idea at the centre of algebra: an equation is a balance, and whatever you do to one side you do to the other. Doing it in your head forces you to plan the order of the moves — undo the addition before the multiplication, gather x on one side before anything else — rather than follow a written routine, and that plan is what carries over to harder equations on paper.
Studies of middle-school algebra find that how students understand the equals sign predicts how well they solve equations. Students who read = as 'the answer comes next' struggle with equations such as 5x + 3 = 2x + 18, while those who read it as 'both sides have the same value' solve them far more often, even after allowing for general maths ability. The balance picture this game is built on is that second reading.
A classroom experiment on learning to solve linear equations found that students who compared two correct ways of solving the same equation — for example, expanding a bracket first versus dividing first — gained more flexible and more accurate skills than students who studied the same methods one after another. That is why the missed-equation list shows the first move for each equation: a different first move is often the quicker route.
Doing the steps mentally adds a working-memory load on top of the algebra, and mental arithmetic research links fluent recall of number facts to freeing that memory for the rest of a problem. The equations here keep the arithmetic to small whole numbers so that the load stays on planning the moves rather than on the sums.
Undo in reverse order. In 3x − 5 = 16 the x was multiplied, then had 5 taken away, so add 5 first and divide last.
With x on both sides, subtract the smaller x term first. 5x + 3 = 2x + 18 becomes 3x + 3 = 18.
For a bracket, divide by the number outside it before anything else when it divides evenly: 3(x − 2) = 21 gives x − 2 = 7.
Check the sign before you press Check. Many answers on Two Steps and Both Sides are negative.
If an answer feels wrong, put it back into the equation. Checking takes two seconds and saves the streak.
Find the number that x stands for, the one value that makes both sides of the equation equal. In x + 7 = 15, x is 8, because 8 + 7 = 15.
Undo the addition or subtraction first, then the multiplication or division. For 3x − 5 = 16, add 5 to both sides to get 3x = 21, then divide by 3 to get x = 7.
Move the x terms to one side first. In 5x + 3 = 2x + 18, subtract 2x from both sides to get 3x + 3 = 18, then subtract 3 and divide by 3: x = 5.
Yes. Each equation is generated from a whole-number answer, so there are no fractions to type. Answers on Two Steps and Both Sides can be negative, which is what the minus key is for.
One Step matches the first equations met in pre-algebra, and Two Steps and Both Sides match the linear equations of a first algebra course. There is no sign-up, so it works as a warm-up in class or at home.
The game shows the first move after a miss. For the full step-by-step working on any equation, including fractions and decimals, use the free equation solver on this site.