To create an equation with infinite solutions, the two sides must be equivalent for all values of \( x \). This means we need to find constants that make the equation true regardless of the value of \( x \).
Starting with the left side of the equation:
\[ 4x + 10 \]
We can express the right side in a way that will ensure both sides are identical. Let's break it down:
Let \( a \) represent the coefficient of \( x \) on the right side, and \( b \) represent the constant.
We want the right side to also equal \( 4x + 10 \). Therefore, we can set:
- The coefficient of \( x \) on the right side to be \( 4 \): \( a = 4 \)
- The constant on the right side must match the constant on the left side: \( b = 10 \)
Thus, we can fill in the blanks with these values:
The completed equation is:
\[ 4x + 10 = 4x + 10 \]
This equation holds true for all \( x \), resulting in infinite solutions.