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LiveMath uses a worksheet-based approach, similar to products like Mathematica or MathCAD. The user enters equations into the worksheet and then uses the built-in functions to help solve them, or reduce them numerically. Workbooks typically contain a number of equations separated into sections, along with data tables, graphs, and similar outputs.
A valid number sentence using a 'less than' symbol: 3 + 6 < 10. A valid number sentence using a 'more than' symbol: 3 + 9 > 11. An example from a lesson plan: [6] Some students will use a direct computational approach. They will carry out the addition 26 + 39 = 65, put 65 = 26 + , and then find that = 39.
In the simple case of a function of one variable, say, h(x), we can solve an equation of the form h(x) = c for some constant c by considering what is known as the inverse function of h. Given a function h : A → B , the inverse function, denoted h −1 and defined as h −1 : B → A , is a function such that
To solve this kind of equation, the technique is add, subtract, multiply, or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated, the other side of the equation is the value of the variable. [ 37 ]
Animation depicting the process of completing the square. (Details, animated GIF version)In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form + + to the form + for some values of and . [1]
Al-Khwarizmi introduced systematic methods for transforming equations, such as moving a term from one side of an equation into the other side. [30] The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in the title of his main treatise .
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