To create an equation with no solution, the two sides of the equation must be equivalent in terms of their structure but contradictory in their constants.
Let's analyze the equation: \[3x - 6 = 3x - ?\]
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If we subtract \(3x\) from both sides, we get: \[ -6 = -? \]
This means for the equation to be contradictory (and therefore have no solution), the value of the constant on the right side must not equal -6.
Now we can analyze the options:
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If ? is -6: \[ -6 = -(-6) \implies -6 = -6 \text{ (a true statement)} \] So, this would create a solution.
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If ? is 6: \[ -6 \neq -6 \text{ (false statement)} \] This would create an equation with no solution.
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If ? is 3: \[ -6 \neq -3 \text{ (false statement)} \] This would create an equation with no solution.
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If ? is -3: \[ -6 \neq -(-3) \text{ (false statement)} \] This would create an equation with no solution.
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If ? is 0: \[ -6 \neq -0 \text{ (false statement)} \] This would create an equation with no solution.
Thus, the values that would create an equation with no solution are:
- 6
- 3
- -3
- 0
Therefore, the choices that would create an equation with no solution are:
- 6
- 3
- -3
- 0
12 answers