Final answer:
The equation 2(2x + 5) = 50 is also true for the same value of x that satisfies the equation 4(2x + 5) = 100 because dividing the original equation by 2 does not change the solution set for x.
Step-by-step explanation:
The equation 4(2x + 5) = 100 is true for a particular value of x because it is a linear equation that can be solved by isolating the variable x. When we attempt to solve this equation, it implies that the expression within the brackets, (2x + 5), multiplied by 4 results in 100. To understand why the equation 2(2x + 5) = 50 is also true for the same value of x, we must perform equivalent operations on both sides of the equation.
Dividing both sides of the original equation by 2 yields 2(2x + 5) = 50, which is a result of the property that if two sides of an equality are divided by the same nonzero number, the resultant equation remains true. This means that for the value of x that satisfies the original equation, dividing the entire equation by 2 will not change the solution set, hence the value of x that satisfies 4(2x + 5) = 100 will also satisfy 2(2x + 5) = 50.