Question

Determine whether the equation is a conditional equation, an identity, or a contradiction.

16y + 2(3 - y) = 5 + 14y + 2

Answer 1

To determine whether the equation is a conditional equation, an identity, or a contradiction, we need to simplify and solve it.

16y + 2(3 - y) = 5 + 14y + 2

Step 1: Distribute the 2 on the left side:

16y + 2(3) - 2y = 7 + 14y

Step 2: Combine like terms on the left side:

16y + 6 - 2y = 7 + 14y

Step 3: Simplify further:

14y + 6 = 7 + 14y

Step 4: Subtract 14y from both sides to eliminate the variable:

6 = 7

Now, looking at the result, we see that we get an incorrect statement: 6 = 7. This is a contradiction because it shows that there is no value of y that will make the equation true.

Therefore, the given equation is a contradiction.