Question

Complete the equation so that it has infinite solutions.(1 point)
4x + 10= blankx + blank

Answer 1

To create an equation with infinite solutions, the left side must be equivalent to the right side. We can achieve this by ensuring that both sides are proportional.

Let's take the equation:

\[ 4x + 10 = Ax + B \]

For the equation to have infinite solutions, the coefficients of \(x\) and the constant terms must be equal when expressed in a comparable form.

1. Set the coefficients of \(x\) equal to each other:
\[ A = 4 \]

2. Set the constant terms equal to each other:
\[ B = 10 \]

Now, substituting these values into the equation, we get:

\[ 4x + 10 = 4x + 10 \]

Thus, the blanks can be filled with:
- The first blank: \(4\)
- The second blank: \(10\)

So, the completed equation is:

\[ 4x + 10 = 4x + 10 \]

This ensures that the equation has infinite solutions.