Math Lesson 9.1.4 - Regular Form of Equations

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Welcome to our Math lesson on Regular Form of Equations, this is the fourth lesson of our suite of math lessons covering the topic of Variables, Coefficients and Constants. First Order Equations with One Variable, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Regular Form of Equations

For now, we will take as true without proof the rule we mentioned above regarding the change in sign when sending a number from one side of the equation to the other. This rule is also applicable for whole terms, not just for constants. For example, the equation

can be expressed in various forms such as

However, the regular form of all equations is

where E(x, y, z) is the equation written in terms of variables x, y, z, etc. From this rule, it is clear that the regular form of the equation in our example therefore is

Example 4

Express the following equations in the regular form.

1. 3 + 4x² = 2y + 7
2. 8 - 2x³ + 5y = 4y - 1

Solution 4

1. We have to send everything on the left side of the equation in order to express it in the regular form. In this process, all terms on the right that change side change also their sign. Thus,
   3 + 4x² = 2y + 7
   3 + 4x² - 2y - 7 = 0
   We can make operations with like terms just as we did in algebraic expressions. Thus,
   3 + 4x² - 2y - 7 = 0
   Therefore, the regular form of the given equation is
   4x² - 2y - 4 = 0
2. Following the same procedure as in (a) yields
   8 - 2x³ + 5y = 4y - 1
   8 - 2x³ + 5y - 4y + 1 = 0
   Completing the operations with like terms yields
   8 - 2x³ + 5y - 4y + 1 = 0
   - 2x³ - y + 9 = 0

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