Question[x.]. Find the missing number so that the equation has infinitely many solutions. $\square$ $x+2=-3 x+2$ Submit

Studdy Solution

STEP 1

1. The equation is linear in terms of $x$ .
2. For the equation to have infinitely many solutions, both sides of the equation must be identical for all values of $x$ .

STEP 2

1. Understand the structure of the equation.
2. Identify the condition for infinitely many solutions.
3. Solve for the missing number.

STEP 3

Understand the structure of the equation. The given equation is:
$\square x + 2 = -3x + 2$
Here, $\square$ represents the missing coefficient of $x$ on the left side.

STEP 4

Identify the condition for infinitely many solutions. For the equation to have infinitely many solutions, the expressions on both sides of the equation must be identical for all values of $x$ . This means:
$\square x + 2 = -3x + 2$
The coefficients of $x$ and the constant terms on both sides must be equal.

STEP 5

Solve for the missing number. Set the coefficients of $x$ equal to each other:
$\square = -3$
Therefore, the missing number is $-3$ .
The missing number is $\boxed{-3}$ .

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