Question

problem 8
the equation $5\left(0.2x + \frac{1}{25}\
ight) = x + \frac{1}{5}$ has infinitely many solutions.
anya creates another equation, $10\left(0.2x + \frac{1}{25}\
ight) = 2x + \frac{2}{5}$, and says it also has infinitely many solutions.
why might she think that?

Explanation:

Anya likely noticed that she multiplied both sides of the first equation by 2, a non-zero constant. Multiplying both sides of an equation with infinitely many solutions by a non-zero constant preserves the property of having infinitely many solutions, as it creates an equivalent equation where both sides simplify to identical expressions for all x.

Answer:

She probably recognized that her new equation is an equivalent form of the first equation (she multiplied both sides of the original equation by 2). Since equivalent equations have the same solution set, and the first equation has infinitely many solutions, she would assume her equation does too.