Final answer:
The inequality 5x - 7/5 ≤ 5x + 2/3 has no solutions because, after canceling out the variable terms and comparing the constants, -7/5 is never less than or equal to 2/3.
Step-by-step explanation:
To solve the inequality 5x - 7/5 ≤ 5x + 2/3, we need to isolate the variable on one side. However, in this case, we notice that the variable terms on both sides of the inequality are the same. To proceed, let's subtract 5x from both sides to get:
-7/5 ≤ 2/3
Now we will convert these fractions to have a common denominator, which is 15, and then compare them:
-21/15 is not less than or equal to 10/15. Therefore, this inequality is false regardless of the value of x. As there is no solution where -7/5 is less than or equal to 2/3, there is no value of x which can satisfy the original inequality.
This means there are no solutions to the given inequality.