Final answer:
Equations A and E have an infinite number of solutions.
Step-by-step explanation:
An equation has an infinite number of solutions when the equation is an identity, meaning that the left side of the equation is equal to the right side for all values of the variable. Looking at the given options, equations A and E fit this criteria. Let's analyze them:
A) 3x - 2(x + 10) = x - 20:
Expanding the expression on the left side gives us 3x - 2x - 20 = x - 20. Simplifying further, we have x - 20 = x - 20, which is true for any value of x. Thus, this equation has infinite solutions.
E) x + x = x + 7:
Combining like terms on both sides gives us 2x = x + 7. Subtracting x from both sides gives us x = 7, which is a specific solution. However, if we substitute x = 7 back into the equation, we get 7 + 7 = 7 + 7, which is true. Therefore, this equation also has infinite solutions.
Therefore, the equations A and E have an infinite number of solutions.
Learn more about Infinite Solutions in Equations