Question

Solve and show all steps used.
-2/5x-9<9/10

Answer 1

To solve the inequality, we need to isolate x on one side of the inequality sign.

Starting with the given inequality:

-2/5x - 9 < 9/10

First, let's add 9 to both sides of the inequality to isolate the term with x:

-2/5x - 9 + 9 < 9/10 + 9

Simplifying:

-2/5x < 9/10 + 90/10

-2/5x < 99/10

Next, let's multiply both sides of the inequality by -5/2 to get rid of the fraction:

-5/2 * -2/5x > -5/2 * (99/10)

Simplifying:

x > -5/2 * (99/10)

x > -495/20

Since -495/20 can be simplified further, let's divide both the numerator and denominator by their greatest common divisor, which is 5:

x > -99/4

Therefore, the solution to the inequality is x > -99/4.