Question

Zahra wants the equation below to have an infinite number of solutions when the missing number is placed in the box.

Answer 1

The answer is -3.

To find this, we simply have to solve the equation and leave only the blank and the parenthesis that it is with on the right side. Then we can divide by the parenthesis. The work for this is done for you below.

____(x - 3) + 2x = -(x - 5) + 4 ----> Distribute the -1 to the parenthesis.

____(x + 3) + 2x = -x + 5 + 4 ----> Simplify

____(x + 3) + 2x = -x + 9 ----> Subtract 2x from both sides

____(x + 3) = -3x + 9 ------> Divide both sides by x + 3

____ = -3.

Answer 2

Let the missing number be 'y'

$= > y(x - 3) + 2x = - (x - 5) + 4 \\ \\ = > y(x - 3) + 2x= - x + 5 + 4 \\ \\ = > y(x - 3) = - x - 2x + 9 \\ \\ = > y(x - 3) = - 3x + 9 \\ \\ = > y = \frac{ - 3(x - 3)}{(x - 3)} \\ \\ = > y = - 3$

$\boxed{Missing \: number = -3}$