Default
Projection

DrDelMath

College Algebra Examples
Equations: Identify and Classify


As you study these illustrations, move your cursor over arrows, equal symbols, icons, and highlighted words.
Always check-in with the wise old owl and his little apprentice by moving your cursor over them.
Study with an active cursor.

 
The definition that pops up when you move the cursor over a highlighted word is what should pop into your mind when you read, hear, or speak that word. The material that pops up when you move the cursor over a light bulb is a suggested strategy for solving the problem. You should always formulate a similar strategy when you attempt to solve a problem. When you move the cursor over an explanation of a step in a solution, the property that pops up is the mathematical justification for taking that action. You must always be able to provide such a justification for every step you take in mathematics.

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 repalaced with 2 but is not true if it is replaced with 3 (or any other number).

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.

3. 3x + 2 < 8
 This is clearly a mathematical statement but it does not contain 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 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 condradiction 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 condradiction 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).