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Let’s go back to the equation .The lowest common denominator of the fractions and is 8. So we’ll multiply the expression with those fractions by 8. Because we must preserve the equality of the equation, we’ll multiply the expression on the other side by 8, too. Now we’ve got .But wait—we just put parentheses back into the equation again. Now what? Simple, we go backto our old friend the Distributive Property once again. Once we multiply each term inside the parentheses by 8, both the parentheses and the fractions will disappear. Sweet.
In order to clear away the fractions from , we can multiply both sides of the equationby which of the following numbers?3 6 9 18A) 6B) 3 and 6
C) 9D) 6 and 18Show/Hide AnswerSummaryComplex, multi-step equations often require multi-step solutions. Before we can begin to isolate a variable, we might need to simplify the equation first. This may mean using the Distributive Property to remove parentheses, or multiplying both sides of an equation by a common denominator to get rid of fractions. Sometimes it requires both techniques.common denominatora number that is a multiple of all of the denominators in a group of fractionsDistributive Propertystates that the product of a number and a sum equals the sum of the individual products of the number and the addends: for all real numbers a, b, and c, a(b+ c) = ab+ acmulti-step equationan equation that requires more than one step to solvevariablea symbol that represents an unknown valueAdditive Inverse Propertystates that every real number added to its additive inverse (or opposite) will equal zero: For all real numbers a, a + (-a) = 0; also called Inverse Property of Additioncoefficienta number that multiplies a variable
equationa statement that describes the equality of two expressions by connecting them with an equals signInverse Operationsoperations that undo or cancel one another, such as addition/subtraction and multiplication/divisionMultiplicative Inverse Propertystates that any number multiplied by 1 over that number equals 1: For all real numbers a, ; also called Inverse Property of MultiplicationProperty of Equalitystates that the equality of an equation is maintained when both sides have the same value added, subtracted, multiplied, or dividedvariablea symbol that represents an unknown value