To complete the equation \( 4x + 10 = \text{blank} \cdot x + \text{blank} \) so that it has infinite solutions, we want the two sides of the equation to be equivalent for any value of \( x \).
One way to do this is to express the right side in terms of the left side. We can choose constants such that the coefficients of \( x \) and the constant terms on both sides are equal.
Let's set the right side as follows:
\[ 4x + 10 = 4x + 10 \]
This means:
- The coefficient of \( x \) on the right side will be \( 4 \).
- The constant term (the blank) on the right side will be \( 10 \).
Thus, we can fill in the blanks:
\[ 4x + 10 = 4x + 10 \]
So, the completed equation is:
\[ 4x + 10 = 4x + 10 \]
This has infinite solutions, as both sides are identical for all values of \( x \).