The solution to the inequality 5x - 1/5 < 6x - 9/10 is x > 7/10. This represents an infinite set of real numbers to the right of 7/10 on the number line.
To solve the inequality 5x - 1/5 < 6x - 9/10, follow these steps:
Combine like terms:
5x - 1/5 < 6x - 9/10.
Add/subtract to both sides to isolate x:
5x < 6x - 7/10.
-x < -7/10.
Divide both sides by the same factor and flip the relation if necessary:
x > 7/10.
So, the solution to the inequality is x > 7/10. This means any value of x greater than 7/10 satisfies the inequality. The process involved combining like terms, isolating the variable, and ensuring the correct direction of the inequality when dividing by a negative number.
This solution represents an infinite set of real numbers, and graphically, it corresponds to all x-values to the right of 7/10 on the number line.