Question $2 x+\square=2(x+10)$ Submit

Studdy Solution

STEP 1

1. The equation $2x + \square = 2(x + 10)$ is asking us to find the missing number that makes the equation have infinitely many solutions.
2. For an equation to have infinitely many solutions, both sides of the equation must be identical after simplification.
3. The equation involves basic algebraic operations, specifically distribution and simplification.

STEP 2

1. Expand the right-hand side of the equation.
2. Compare both sides of the equation to determine the missing number.
3. Verify that the equation has infinitely many solutions with the found number.

STEP 3

Expand the right-hand side of the equation:
$2(x + 10) = 2x + 20$

STEP 4

For the equation to have infinitely many solutions, both sides must be identical.
Compare the left-hand side $2x + \square$ with the expanded right-hand side $2x + 20$ .
The missing number $\square$ must be equal to 20.

STEP 5

Verify that with $\square = 20$ , the equation becomes:
$2x + 20 = 2x + 20$
Both sides are identical, confirming infinitely many solutions.
The missing number is:
$\boxed{20}$

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