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Math  /  Algebra

Question㮁 Find the missing number so that the equation has infinitely many solutions. 2x−4−7x=□x−42 x-4-7 x=\square x-4 Submit

Studdy Solution

STEP 1

1. The equation is 2x−4−7x=□x−42x - 4 - 7x = \square x - 4.
2. For the equation to have infinitely many solutions, both sides of the equation must be identical after simplification.

STEP 2

1. Simplify the left side of the equation.
2. Set the simplified left side equal to the right side.
3. Determine the value of the missing number (□\square) that makes both sides identical.

STEP 3

Simplify the left side of the equation:
2x−4−7x 2x - 4 - 7x
Combine like terms:
(2x−7x)−4=−5x−4 (2x - 7x) - 4 = -5x - 4

STEP 4

Set the simplified left side equal to the right side of the equation:
−5x−4=□x−4 -5x - 4 = \square x - 4

STEP 5

For the equation to have infinitely many solutions, the coefficients of xx and the constant terms on both sides must be equal. This means:
−5x=□x -5x = \square x
Thus, the missing number must be:
□=−5 \square = -5
The missing number is −5\boxed{-5}.

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