Question

Complete the equation so it has infinitely many solutions.

4x + 7 = 4(x + 3) –

Answer 1

To complete the equation \( 4x + 7 = 4(x + 3) - ? \) so that it has infinitely many solutions, we need the left side to equal the right side for all values of \( x \).

First, let's simplify the right side:
\[
4(x + 3) = 4x + 12.
\]
Substituting this back into the equation yields:
\[
4x + 7 = 4x + 12 - ?.
\]

For the equation to have infinitely many solutions, the constant terms on both sides must be equal after simplification. This means we want the following to hold:
\[
7 = 12 - ?.
\]

Now rearranging gives:
\[
? = 12 - 7 = 5.
\]

Therefore, the equation with infinitely many solutions is:
\[
4x + 7 = 4(x + 3) - 5.
\]

In simpler form, this can be written as:
\[
4x + 7 = 4x + 12 - 5,
\]
which simplifies to:
\[
4x + 7 = 4x + 7.
\]

This confirms that the complete equation is:
\[
4x + 7 = 4(x + 3) - 5.
\]