Introduction to Algebraic equation: Algebra is the study of set of laws of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. An expression is algebraic if it involves a finite grouping of numbers and variables and algebraic operations (including addition, subtraction, and multiplication, division, raising to a power, and extracting a root).An algebraic equation is in the form of X+Y=10 format.,and one important thing in the algebraic equation is both the sides are equal. The algebraic equations are the basis of a number of areas of modern mathematics: Algebraic number theory is the study of (univariate) algebraic equations over the rationals. Galois theory has been introduced by Évariste Galois for getting criteria deciding if an algebraic equation may be solved in terms of radicals. In field theory, an algebraic extension is an extension such that every element is a root of an algebraic equation over the base field. Transcendence theory is the study of the real numbers which are not solutions to an algebraic equation over the rationals. A Diophantine equation is a (usually multivariate) polynomial equation with integer coefficients for which one is interested in the integer solutions. Algebraic geometry is the study of the solutions in an algebraically closed field of multivariate polynomial equations. Types of algebraic equations: Two important types of algebraic equations are important, there are given below: 1. Quadratic equations, and 2. Linear equations. Those above two equations are the very important equations in the algebra. Explanations: Linear equations, in the form y = ax + b, and quadratic equations, in the form y = ax^2bx + c. When the equation is true statement means the substitution of the solution (numerical value) to the variable is same. In some cases it may be found using a procedure; in others the equation may be rewritten in simpler form. Algebraic equations are predominantly useful for modeling real-life phenomena. Developing an Algebraic Equation: One or both of the expressions may contain variables. Solving an equation means finding the value of the variable. Example 1: Solve the equation: 4x-2=6 Both sides of the algebraic equation must be equal,the steps are as follows,. Step 1: First, add 2 on both sides of the equation so that 4x-2+2=6+2 or 4x=8. If we multiply (or divide) one side by a measure, we must multiply (or divide) the other side by that same quantity. Step 2: To solve this equation we need to divide both sides by 8. The equation would become 4x/4 = 8/4. Step 3: When simplified, this would become x = 8/4 or x = 2. It is possible to replace with the value of x back into the original equation 4 * 2 - 2 = 6. Answer is 6. Example 2: Solve X*20=40 X*(20/20)=40/20 X*1=2*1 X=2 Example 3: Solve the following equation: 15x-18=9x-24 Solution: Divide both sides by 3 5x-6=3x-8 Subtract by 3x on both sides 2x-6=-8 2x-6+8=0 2x+2=0 2x = -2 X = -1 These all are the above equations and example problems develop and make clear about the algebraic equations Understand more on about solving algebra word problems and its Illustrations. Between, if you have issue on these subjects factoring polynomials degree 3, Please discuss your feedback.
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