Question

Solve the inequality. Present the solution on a (1)/(5)<=(1)/(2)x-(1)/(7)<=(7)/(4)

Answer 1

To solve the inequality (1)/(5)<=(1)/(2)x-(1)/(7)<=(7)/(4), we need to isolate the variable x and combine the fractions. The solution to the inequality is (17)/(35)<=x<(43)/(28).

Step-by-step explanation:

To solve the inequality (1)/(5)<=(1)/(2)x-(1)/(7)<=(7)/(4), we need to isolate the variable x.

1. First, we subtract (1)/(7) from both sides of the inequality: (1)/(5)-(1)/(7)<=(1)/(2)x-(1)/(7)-(1)/(7)<=(7)/(4)-(1)/(7).
2. This simplifies to (7)/(35)-(5)/(35)<=(1)/(2)x-(2)/(7)<=(47)/(28)-(4)/(28).
3. Next, we combine the fractions on both sides to get (2)/(35)<=(1)/(2)x-(2)/(7)<(15)/(28).
4. We can then find a common denominator and simplify the inequality: (2)/(35)<=(7)/(14)x-(10)/(14)<(15)/(28).
5. Finally, we can solve for x by isolating the variable: (2)/(35)+(10)/(14)<=(7)/(14)x-(10)/(14)+(15)/(28)<(15)/(28)+(10)/(14).
6. This further simplifies to (17)/(35)<=(7)/(14)x<(43)/(28).

Therefore, the solution to the inequality is (17)/(35)<=x<(43)/(28).