Question

Complete the equation so that it has infinite solutions.(1 point)
4x+10= x +
Put the response into the equation I have given.

Answer 1

To have infinite solutions, the equation must be an identity, meaning both sides are equal for all values of \( x \).

Starting with the equation:

\[
4x + 10 = x + \text{?}
\]

We can rearrange it to find out what goes in place of the question mark. To do this, we can isolate \( x \) terms on one side:

1. Subtract \( x \) from both sides:
\[
4x - x + 10 = \text{?}
\]

2. This simplifies to:
\[
3x + 10 = \text{?}
\]

For the equation to hold for all \( x \), the right side must equal the left side. Therefore, we can set it as:

\[
\text{?} = 3x + 10
\]

This doesn't simplify the equation because we need \( \text{?} \) to be a constant when \( x \) is removed. For this, both sides need to be identical. In this case, that's when we have the coefficient of \( x \) as \( 0 \).

So, using the previously rewritten equation, we can determine that:

To achieve this, we can set the equation so both sides have equal constant values. Rearranging gives a clue:

Setting it so that:
\[
4x + 10 = x + 10 + 3x
\]
This would lead to:
\[
4x + 10 = 4x + 10
\]

Therefore, the complete equation you are looking for is:

\[
4x + 10 = x + 10 + 3x
\]

Thus, you put \( 10 + 3x \) replacing the question mark, and this gives us infinite solutions:

The final answer is:

\[
4x + 10 = x + 10 + 3x
\]