Final answer:
Mario is correct to use the distributive property to solve the equation 4(5x+5)=40. The method involves multiplying each term by 4, then isolating and solving for x to eventually obtain x = 1.
Step-by-step explanation:
Mario is correct in saying that using the distributive property to solve the equation 4(5x+5)=40 is a suitable method. To do this, we apply the distributive property by multiplying each term inside the parentheses by 4, which gives us 20x + 20 = 40. After distributing, we subtract 20 from both sides to obtain 20x = 20. Finally, we divide both sides by 20 to solve for x, resulting in x = 1.
Using the distributive property helps to simplify the equation step by step, ensuring that the process of solving it is clear. Moreover, understanding that multiplication or division by the same number on both sides of an equation does not change equality is vital in the process of solving algebraic equations. Remembering that operations need to apply to every term within the parentheses is a foundational aspect of the distributive property. To reiterate, the equality of the equation is maintained as long as the operations are performed on both sides.