Working with formulas > Equations


Formulas such as y = 2 x + 3 , or a + 4 b c = 15 , or 6 x + 10 = 2 x 8 are called equations. You can look for values (or combinations of values) that satisfy the equation. This is called solving an equation.

Equations can be solved systematically by rewriting them. Especially for equations with one variable this is often done. You can use algebraic methods like:

  • the balance method, in which, on both sides of the equals sign, you

    • add or subtract the same amount;

    • multiply or divide by the same number (but not by 0 ) on both sides of the equals sign.

  • the reversing method, in which you undo calculations by doing the opposite:

    • you undo addition by subtraction (and vice versa);

    • you undo multiplication by division (and vice versa);

    • you undo powers by extracting roots (and vice versa).

  • factorization, where you use the fact that a b = 0 is equivalent to a = 0 b = 0 .
    The sign means that you should read this expression as a = 0 and/or b = 0 (so a = 0 or b = 0 or both).

When algebraic methods do not work, you can think of iteration: you search for an answer by decreasing the search area. Your graphic calculator has several built-in routines for this.

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