143k views
1 vote
The equation 4(2x + 5) = 100 is a true equation for a particular value of x. Explain why 2(2x + 5) = 50 is also true for the same value of x.

1 Answer

4 votes

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.

User Anton Khirnov
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories