Question

Here is an equation that is true for all values of x: 5(x+2) = 5x + 10. Elena saw this equation and says she can tell 20(x + 2) + 31 = 4(5x + 10) + 31 is also true for any value of x. How can she tell? Explain your reasoning.

Answer 1

The equations are the same. See Explanation for further detail.

Explanation:

Starting out with the equation

5(x+2) = 5x + 10

Lets multiply both sides by 4

20(x+2) = 4(5x + 10)

Now we can add 31 to both sides of the equation.

20(x+2) + 31 = 4(5x+10) + 31

This is Elena's new equation.

By making the same change to both sides of the equation, the equation remains unchanged, and therefore will have the same results as the original equations. Thus, since the functions are equal, Elena can tell that her new equation is true.