To create an equation with infinite solutions, both sides must be equivalent expressions.
You want to manipulate the equation \(4x + 10 = _x + _\) to make it true for all values of \(x\).
Here's one way to do it:
Set the blank on the left side to match the right side. We can rewrite the right side as the same expression as the left.
Let the blanks be:
- For the first blank (coefficient of \(x\)), use \(4\)
- For the second blank (constant term), use \(10\)
So the completed equation is: \[ 4x + 10 = 4x + 10 \]
This equation will have infinite solutions because both sides are identical for any value of \(x\).
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