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Math  /  Algebra

QuestionFind the missing number so that the equation has no solutions. −4x−12=□x+16-4 x-12=\square x+16
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Studdy Solution

STEP 1

1. The equation is linear and can be manipulated using algebraic operations.
2. We need to find a condition where the equation has no solutions, which typically occurs when we end up with a contradiction.

STEP 2

1. Simplify and rearrange the equation.
2. Determine the condition for no solutions.
3. Solve for the missing number.

STEP 3

Start with the given equation:
−4x−12=□x+16 -4x - 12 = \square x + 16
Our goal is to rearrange the equation to isolate terms involving x x on one side and constants on the other.

STEP 4

Rearrange the equation by moving all terms involving x x to one side and constants to the other side:
−4x−□x=16+12 -4x - \square x = 16 + 12
Combine like terms:
(−4−□)x=28 (-4 - \square)x = 28

STEP 5

For the equation to have no solutions, the coefficient of x x must be zero, leading to a contradiction. This means:
−4−□=0 -4 - \square = 0

STEP 6

Solve for the missing number by setting the coefficient of x x to zero:
−4−□=0 -4 - \square = 0
Add 4 to both sides:
□=−4 \square = -4
The missing number that makes the equation have no solutions is −4 \boxed{-4} .

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