equation: an equation is a mathematical statement that two expressions are equal.expression: groups of terms connected by addition and subtraction.term: a single number, or variables and numbers connected by multiplication.This number is called the coefficient of the variable. coefficient: Sometimes a variable is multiplied by a number.variables: variables are symbols that stand for an unknown quantity they are often represented with letters, like x, y, or z.Use Properties of Equality to Isolate Variables and Solve Algebraic Equationsįirst, let us define some important terminology: To check, substitute 9 for x in the original equation.Steps with an end in sight. Multiplying both sides of the equation by (x-4)(2x+3) we get ![]() Solution Multiply both sides of the equation by (3x-4).ĮXAMPLE Solve the following equation and check: Solution Multiply both sides of the equation by 12x^2.ĮXAMPLE Solve the equation (2x)/(3x-4)-2 = 0 ![]() The values of the variable that do not satisfy the original equation are called extraneous roots.ĮXAMPLE Solve the equation 3/(4x)-1/(3x^2) = 5/(6x) In all Such cases the elements in the solution set must be checked in the original equation. The ‘mulling equation may have a solution set with elements that do not satisfy the original equation. the resulting equation may not be equivalent to the original equation. When an equation is multiplied by the LCD (which is a polynomial in the variable). When an equation involves fractions, it can be put in a simpler form when both sides of the equation are multiplied by the LCD of all the fractions in the equation. Many problems require the solution of a formula for one of the letters involved.ħ.7 Equations Involving Algebraic Fractions Formulas may be considered special types of literal equations. They are widely used in many fields of study. To check, substitute a+2 for x in the original equation.įormulas are rules expressed in symbols or literal numbers. If (a-4) ≠ 0, that is, a ≠ 4, we can divide both sides of the equation by (a-4) to get Click on "Solve Similar" button to see more examples.ĮXAMPLE Solve the following equation for x and check: Let’s see how our step by step math solver solves this and similar problems. Note For any value for a ≠ 2/3 the value of x is 2, When a= 2/3, the equation becomes an identity, that is, a statement that is true for all values of x. ![]() If (3a-2) ≠ 0, that is a ≠ 2/3, we can divide both sides of the equation by (3a-2) to get Note When a=-2, we have a false statement,ĮXAMPLE Solve the following equation for x: 3ax+4 = 2x+6a. If a+2 ≠ 0, that is a≠ -2, we can divide both sides of the equation by (a+2) to get Simplify the answer and check by substituting the value you obtained for the variable in the original equation.ĮXAMPLE Solve the following equation for x: 2y-3x=8.ĮXAMPLE Solve the following equation for x: Factor the variable from the terms that have the variable as a factor and then divide both sides of the equation by the coefficient of the variable. To find the solution set of a literal equation, form an equivalent equation with all the terms that have the variable as a factor on one side of the equation and those terms that do not have the variable as a factor on the other side. we obtain corresponding values for the variable. We can solve for one of the literals, called the variable, in terms of the other literals, Thus by assigning values for those literals. Some equations, called literal equations, involve more than one literal number.
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