5х-2/4-3-х/5>1-х/10

To solve the inequality, we need to simplify both sides and isolate the variable, "x."

Starting with the left side of the inequality:

5x - 2/4 - 3 - x/5

First, let's simplify the expression within the parentheses:

-2/4 - 3 = -1/2 - 3 = -7/2

Now, let's combine the terms:

5x - 7/2 - x/5

To combine the terms with different denominators, we need to find a common denominator. In this case, the common denominator is 10:

5x - (7/2)(5/5) - (x/5)(2/2)

= 5x - 35/10 - 2x/10

Now, we can combine the terms:

5x - 35/10 - 2x/10

= (5x - 2x)/10 - 35/10

= 3x/10 - 35/10

= (3x - 35)/10

Now, the inequality becomes:

(3x - 35)/10 > 1 - x/10

Multiply both sides of the inequality by 10 to eliminate the denominators:

10(3x - 35)/10 > 10(1 - x/10)

Simplifying both sides:

3x - 35 > 10 - x

Add x to both sides:

3x + x - 35 > 10

Combine like terms:

4x - 35 > 10

Add 35 to both sides:

4x > 10 + 35

4x > 45

Finally, divide both sides by 4 to isolate x:

x > 45/4

Therefore, the solution to the inequality is x > 11.25.