Question

Complete the equation so that it has infinite solutions. (1 point)

4x+10 = blank x+ blank

Answer 1

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:

1. The coefficient of \( x \) on the right side will be \( 4 \).
2. 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 \( x \).