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Conditional equations

We say that an equation is a conditional equation if it is made true by the input of only one value for the variable. 4x - 8 = 20 is an example of this. 7 is the only value which will make the equation true. When we enter 7 into the variable x, we multiply that 7 by the number 4, and we get 28. Next, we subtract that 28 by 8 and we get 20. Therefore, the condition upon which the equation becomes "true" is upon the input of the value of 7 into the variable. But suppose we enter 4 into the variable. We would multiply the input value 4 by 4 and get 16. 16 - 8 gives us 8. This makes the statement false, because 8 does not equal 20.

Suppose we enter 6 instead. We would multiply 6 x 4. This would give us 16. This also would be incorrect because 16 does not equal 20. As mentioned before, the only value that would make the statement true (that is, the sole condition upon which the equation would become true) is the input of the value of 7 in the variable x. Therefore, it is a conditional equation, because a conditional equation is an equation which is made true upon the sole condition of the input of only one value.

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