When solving an equation by clearing fractions, such as $\frac{1}{5}x + 10 = 50$, what is the mandatory requirement regarding the integer terms (10 and 50) when multiplying both sides of the equation by the Least Common Denominator (5)?

True or False: When clearing decimals from a logistics formula—such as ${}0.5x + 100 = 500$—by multiplying both sides by 10, the Distributive Property requires that every single term in the equation, including the integers 100 and 500, must be multiplied by 10.

Clearing Fractions and the Distributive Property

A payroll specialist uses the equation $\frac{1}{10}S + 500 = 2500$ to calculate a company's salary structure. To clear the fraction, the specialist multiplies both sides of the equation by the least common denominator (10). According to the Distributive Property, the specialist must multiply ____ term in the equation by 10 to ensure the equation remains balanced.

In your role as an inventory analyst, you often use algebraic formulas with fractions to calculate storage capacity. When clearing fractions from these equations to simplify your work, you must remember the rules of algebraic operations. Match each concept related to clearing fractions with its correct description based on the requirement to multiply every term.