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Fill in the blanks so that the resulting equation has no solutions.
___ + ___ = ___ + ____
p 2p 3p 4p 5p 6p 7p 8p 0 1 2 3 4 5 6 7 8

 Nov 4, 2023
 #1
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To make an equation have no solutions, the two sides of the equation must be unequal no matter what values are plugged in for the variables. One way to do this is to have the same variable on both sides of the equation, but with different coefficients. For example, the equation x+2x=3x+1 has no solutions, because if we plug in any value for x, the two sides of the equation will never be equal.

Another way to make an equation have no solutions is to have a contradiction on one side of the equation. For example, the equation x+1=0 has no solutions, because it is impossible for any number plus 1 to equal 0.

To fill in the blanks in the equation $___ + ___ = ___ + ____$ so that it has no solutions, we can use either of these methods.

Method 1:

4p + 3p = 7p + 0

This equation has no solutions because it has the same variable on both sides of the equation, but with different coefficients.

Method 2:

p + 1 = 0

This equation has no solutions because it is impossible for any number plus 1 to equal 0.

Therefore, the completed equation is either:

4p + 3p = 7p + 0

or:

p + 1 = 0

 Nov 4, 2023

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