Final answer:
The equation 8k +14 = 14 -13k − 5k simplifies to 26k = 0, which means there is one unique solution, k = 0.
Step-by-step explanation:
To determine how many solutions the equation 8k +14 = 14 -13k − 5k has, we need to simplify and solve for k. First, let's combine like terms on the right side of the equation:
- 14 -13k - 5k becomes 14 -18k.
Now, our equation is 8k + 14 = 14 -18k. Next, let's add 18k to both sides to get all the k terms on one side:
- 8k + 18k + 14 = 14; this simplifies to 26k + 14 = 14.
Then, subtract 14 from both sides to isolate the k term:
- 26k + 14 - 14 = 14 - 14; which simplifies to 26k = 0.
Finally, divide both sides by 26 to solve for k:
- 26k / 26 = 0 / 26; this yields k = 0.
Therefore, the equation has one unique solution, which is k = 0.