Linear Equations and Inequalities - XYZ Custom Plus

136Chapter 2 Linear Equations and InequalitiesNoteOur original equationhas denominators of3, 2, and 4. The LCDfor these three denominators is12, and it has the property thatall three denominators will divideit evenly. Therefore, if we multiplyboth sides of our equation by 12,each denominator will divide into12 and we will be left with anequation that does not contain anydenominators other than 1.mEthOD 2 Eliminating the fractions in the beginning.12 2 _3 x + 1 _2 = 12 − 3 _4 Multiply each side by the LCD 1212 2 _3 x + 12 1 _2 = 12 − 3 _4 Distributive property on the left side8x + 6 = −98x = −15x = − 15 _8MultiplyAdd −6 to each sideMultiply each side by 1 _8As the third line in Method 2 indicates, multiplying each side of the equation bythe LCD eliminates all the fractions from the equation.As you can see, both methods yield the same solution.propertyBecause division is defined as multiplication by the reciprocal, multiplying bothsides of an equation by the same number is equivalent to dividing both sidesof the equation by the reciprocal of that number; that is, multiplying each side_of an equation by 1 and dividing each side of the equation by 3 are equivalent3operations. If we were to solve the equation 3x = 18 using division instead ofmultiplication, the steps would look like this:3x = 18_ 3x3 = _ 183x = 6Original equationDivide each side by 3DivisionUsing division instead of multiplication on a problem like this may save yousome writing. However, with multiplication, it is easier to explain “why” weend up with just one x on the left side of the equation. (The “why” has todo with the associative property of multiplication.) My suggestion is that youcontinue to use multiplication to solve equations like this one until you understandthe process completely. Then, if you find it more convenient, you canuse division instead of multiplication.Getting Ready for ClassAfter reading through the preceding section, respond in your ownwords and in complete sentences.1. Explain in words the multiplication property of equality.2. If an equation contains fractions, how do you use the multiplicationproperty of equality to clear the equation of fractions?3. Why is it okay to divide both sides of an equation by the same nonzeronumber?4. Explain in words how you would solve the equation 3x = 7 using themultiplication property of equality.Answer8. −2