DrDelMath

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Determine which of the following are equations. If it is an equation, determine whether it is an identity, a conditional equation or a contradition.

1. 3x + 2 = 8
This is clearly a mathematical statement and it contains an = symbol. Therefore it is an equation.
It is a conditional equation because the equation is true if the variable is replaced with 2 but is not true if the variable is replaced with 3 (or any number other than 2).

2. 3x + 2
This is clearly a mathematical expression but is not a mathematical statement and it does not contains an = symbol. Therefore it is not an equation.

4. x² = -1
This is clearly a mathematical statement and it contains an = symbol. Therefore it is an equation.
It is a condradiction because the square of any number is positive. That means this equation is false for all possible real values of the variable.

5. Drinking and driving = trouble
This is not a mathematical statement. Therefore it is not an equation.

6. 3 + 7 = 5
This is clearly a mathematical statement and it contains an = symbol. Therefore it is an equation.
It is a contradiction because it is a false statement for all values of variables (there are no variables).

7. 3 + 7 = 10
This is clearly a mathematical statement and it contains an = symbol. Therefore it is an equation.
It is an identity because it is a true statement for all values of variables (there are no variables).

8. x + x = 2x
This is clearly a mathematical statement and it contains an = symbol. Therefore it is an equation.
It is an identity because it is a true statement for all values of variable.

9. |5x - 3| = -1
This is clearly a mathematical statement and it contains an = symbol. Therefore it is an equation.
It is a contradiction because the absolute value of any number is positive. That means this equation is false for all values of the variable.

10. x = y
This is clearly a mathematical statement and it contains an = symbol. Therefore it is an equation.
It is a conditional equation because it is true for some values of the variables x and y (e.g. x = 47 and y = 47) but is false for other values of the variables (e.g. x = 23 and y = 7).