Sizu Riatto
Algebra · Chapter 6

Balance an Equation Step by Step

An equation is a balance. Whatever you do to one pan, do to the other, and it stays level until the letter stands alone.

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Opens on Chapter 6’s example: 3x + 5 = 20: three bags of x and 5 weights against 20 weights.

a·x + b = c·x + d
Enter your numbers, then press Work it out.

How it works

Each move does the same thing to both pans. First, if there are boxes on both sides, take the smaller number of boxes off both (al-Khwarizmi called this al-muqabala, balancing). Then move the loose weights: take them off both pans, or, if the letter side has some taken away, add them back to both (al-jabr, restoring, which gave algebra its name). Last, divide both pans by the number of boxes. If the boxes cancel and the pans still differ, no number works; if they match, every number works. The check puts the answer back into both sides of the first line.

From the book, Chapter 6. x + 9 = 23 gives 14; p − 15 = 40 gives $55; 4t = 52 gives $13; b ÷ 6 = 7.50 gives $45; 50 + x = 29 + 2x gives 21 (take one x off both sides first); and x − 8 = 30 is 38, not Teo’s 22. Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. The algebra is done with exact fractions, so 1/3 stays 1/3; decimals are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.