Question

Complete the equation so that it has infinite solutions.(1 point)
4x+10=__x+__
put the answers in the blank spots

Answer 1

To make the equation \(4x + 10 = \_\_x + \_\_\) have infinite solutions, we need the two sides to be equivalent for all values of \(x\).

The left side is \(4x + 10\). We want the right side to also be equivalent to this expression.

Let’s express the right side similarly. We can set it as:

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

For the equation to hold true for all \(x\), the coefficients of \(x\) and the constant terms must be equal:

1. Coefficients of \(x\): \(k = 4\)
2. Constant terms: \(c = 10\)

Thus, filling in the blanks with these values gives us:

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

So, the answers to fill in the blanks are:

**4** and **10**.