Find the missing number so that the equation has infinitely many solutions.–4x+=–2(2x+1)

Sure, let's solve this step by step:

1. First, let's simplify the equation. The equation given is –4x + _ = –2(2x + 1).

2. Distribute the –2 on the right side of the equation: –2 * 2x is –4x and –2 * 1 is –2. So, the equation becomes –4x + _ = –4x – 2.

3. For the equation to have infinitely many solutions, the expressions on both sides of the equation must be equal. This means that whatever we add to –4x on the left side must make it equal to –4x – 2 on the right side.

4. The only number that would make these two sides equal is -2. So, the missing number is -2.

Therefore, the equation –4x - 2 = –4x - 2 has infinitely many solutions.