Final answer:
The equation has no solution.
Step-by-step explanation:
To determine the number of solutions for the equation 5(w−1)−2=5w+7, we can simplify it by distributing and combining like terms.
Starting with the left side, 5(w−1)−2 becomes 5w - 5 - 2 = 5w - 7.
Now, comparing the simplified equation 5w - 7 = 5w + 7, we notice that the variable w appears on both sides. This means that no matter what value we assign to w, the equation will always be false. Therefore, the equation has no solution (option A).