Final answer:
To eliminate fractions in an algebraic equation, you must multiply each term by the least common multiple (LCM) of the denominators. In the provided example, each term must be multiplied by 2 to achieve whole-number coefficients, thus eliminating fractions and simplifying the equation.
Step-by-step explanation:
The question revolves around the concept of eliminating fractions in an algebraic equation by multiplying each term by a common multiple. This is an essential algebraic technique that simplifies equations and makes them easier to solve. To determine what each term of the equation should be multiplied by to eliminate fractions, it is essential to look at the denominators of the fractions present. In the provided example, the denominators are 1 (implicit for whole numbers) and 0.5. The least common multiple (LCM) of these denominators must be found to eliminate the fractions.
In finding the LCM, we recognize that 0.5 is equivalent to ½ in fraction form. The LCM of 2 (denominator of ½) and 1 is 2. Thus, by multiplying each term of the equation by 2, the fractions are eliminated, resulting in whole-number coefficients. This is demonstrated in the provided reference where 2 × 10 = 20 simplifies to 20 =, and 2×2×Qburgers + 2×0.5×Qbus tickets simplifies to 4×Qburgers + 1×Qbus tickets, effectively eliminating the fraction.
After eliminating the fractions and simplifying, you proceed with regular algebraic solving methods, checking to ensure the solution is reasonable. This step is in compliance with the standard mathematical process as outlined in steps 6 and 7 of the provided information. Thus, the conclusion is to multiply by 2 to eliminate the fractions and simplify the equation.