To create an equation with infinite solutions, both sides of the equation must be identical.
Starting from the left side:
\[ 4x + 10 \]
We want to create an expression on the right side that is exactly equal to \( 4x + 10 \).
Let’s set up the right side as follows:
\[ x + C \]
To find \( C \), we need to make the expressions equal for all \( x \):
\[ x + C = 4x + 10 \]
To isolate \( C \), we can rearrange the equation:
Subtract \( x \) from both sides:
\[ C = 4x - x + 10 \]
This simplifies to:
\[ C = 3x + 10 \]
However, since we want an equation consistent for any \( x \), we can actually match our constant terms appropriately over for \( x \) added.
If we take any standard form where both coefficients match:
Let’s set \( C = 10 \) and equate it fully by expressing:
So let’s say,
\[ x + 10 \]
So we can represent that interpolation through:
The equation that provides infinite solutions could be:
\[ 4x + 10 = x + 10 = 3x + 10 \]
Therefore,
We can concisely say to fill the given year through,
Thus, the completed equation is:
\[ 4x + 10 = x + 10 \]
The key relation can hence be summarized to derive instances leading to infinite solutions.