Question

Find the missing number so that the equation has infinitely many solutions. 4x–18–7x= – 3x+_

Answer 1

To find the missing number such that the equation \(4x - 18 - 7x = -3x + \_\) has infinitely many solutions, we first simplify the left side of the equation.

Starting with the left side:
\[
4x - 18 - 7x = -3x - 18
\]

So, we rewrite the entire equation:
\[
-3x - 18 = -3x + \_
\]

For this equation to have infinitely many solutions, the two sides of the equation must be identical. Thus, we set the constant terms equal to each other:
\[
-18 = \_
\]

Therefore, the missing number is:
\[
\boxed{-18}
\]

This ensures that the equation \(4x - 18 - 7x = -3x - 18\) holds true for infinitely many values of \(x\).